Exhibit d.5

NUVEEN SENIOR INCOME FUND

VARIABLE RATE TERM PREFERRED SHARES

ANNEX 1 TO THE PURCHASE AGREEMENT

AS AMENDED AND EFFECTIVE NOVEMBER 30, 2015

Explanatory Note: The following As-Amended Annex 1 to the Purchase Agreement, effective as of November 30, 2015 (the “As-Amended Annex 1”), replaces in its entirety the Annex 1 to the Purchase Agreement attached to the Statement Establishing and Fixing the Rights and Preferences of Variable Rate Term Preferred Shares (the “Statement”), which was dated and originally filed with the Secretary of the Commonwealth of Massachusetts on December 27, 2013. Effective November 30, 2015, all references to “Annex 1” in the Statement and any Appendix thereto shall be deemed to refer to the As-Amended Annex 1. The parties to the Purchase Agreement have agreed among themselves that the Fund will pay the Increased Rate on the VRTP Shares, and redeem all or a portion of the VRTP Shares at the Mandatory Redemption Price, if the terms and conditions of the As-Amended Annex 1 so provide. The As-Amended Annex 1 is not a part of the Statement or any Appendix thereto and is being filed solely for informational purposes. Capitalized terms not defined in this Explanatory Note shall have the meanings ascribed to them in the Statement.

NUVEEN SENIOR INCOME FUND

ANNEX 1 TO THE PURCHASE AGREEMENT

ADDITIONAL INCREASED RATE EVENTS

AND

ADDITIONAL MANDATORY REDEMPTION EVENTS

Variable Rate Term Preferred Shares

As Amended and Effective November 30, 2015

WHEREAS, the Fund has authorized the issuance pursuant to the Statement to the Purchasers of its Variable Rate Term Preferred (VRTP) shares;

WHEREAS, this Annex reflects the agreement among the Fund, the Purchasers and the Agent, as parties to the Purchase Agreement, with respect to certain events, the occurrence of which shall cause the Fund to pay, subject to the terms and conditions of this Annex, the Increased Rate on VRTP Shares;

WHEREAS, this Annex reflects the agreement among the Fund, the Purchasers and the Agent with respect to certain events, the occurrence of which would cause the Fund to redeem, subject to the terms and conditions of this Annex, at the Mandatory Redemption Price, all or a portion of the VRTP Shares;

NOW, THEREFORE, in consideration of the respective agreements contained herein, the parties hereto agree as follows:

Section 1. Definitions

Any capitalized term not defined herein shall have the meaning ascribed to such term in the Statement. The following terms, as used herein, shall have the following meanings:

“Additional Increased Rate Events” means the events listed in Section 2(a) of this Annex.

“Additional IRE Cure Date” means the date that is five (5) Business Days after the occurrence of a particular event, circumstance or failure that triggers an Additional Increased Rate Event; provided; that solely in respect of any Additional Increased Rate Event set forth in clause (3) or (5) of Section 2(a), if by the fifth (5th) Business Day after the occurrence of such Additional Increased Rate Event (the “IRE Certification Date”), the Fund delivers to the Designated

Owners of the VRTP Shares a certificate signed by a duly authorized officer of the Fund (i) certifying that (x) the Fund has entered into corrective trades in respect of Fund Assets which upon the settlement thereof shall fully cure such Additional Increased Rate Event, and (y) such corrective trades shall settle no later than the day which is twenty (20) days following such IRE Certification Date, and (ii) specifying the identity and Market Value of the Fund Assets which are the subject of such corrective trades, then the Additional IRE Cure Date for such Additional Increase Rate Event shall be extended to the twentieth (20th) day following such IRE Certification Date.

“Additional Mandatory Redemption Event” means the occurrence, without the unanimous affirmative consent or waiver, in writing, of the Designated Owners of all Outstanding VRTP Shares, of any of the following events:

(a) an Amendment Event, Credit Quality Failure, Investment Policies and Restrictions Failure, Lien Failure, or an Investment Policies Amendment Event occurs and such failure or event is not cured as of the Additional MRE Cure Date therefor;

(b) a Senior Security Failure or Derivative Transaction Event occurs and such failure or event is not cured or waived within five (5) Business Days after the occurrence of such failure or event, other than as a result of the redemption required by Section 2.5(b)(iii) of the Statement; or

(c) (i) the Fund challenges in writing the validity or the enforceability of the Credit Agreement, (ii) any amounts due and payable in respect of Advances have been accelerated as a result of an Event of Default thereunder, or (iii) the Credit Agreement terminates prior to the Term Redemption Date or otherwise ceases to be in full force or effect for any reason or the Purchasers or their Affiliates provide less than fifty-one percent (51%) of the financing thereunder, unless such Credit Agreement has been replaced by any Proposed Financing for which the Purchasers or their Affiliates provide at least fifty one per cent (51%) of such Proposed Financing.

“Additional MRE Cure Date” means a date that is thirty (30) days after the occurrence of a particular event, circumstance or failure that triggers an Additional Mandatory Redemption Event; provided that solely in respect of any Additional Mandatory Redemption Event set forth in clause (a) of the definition thereof relating to an Investment Policies and Restriction Failure or a Lien Failure, if by the thirtieth (30^th) day after the occurrence of such Additional Mandatory Redemption Event (the “MRE Certification Date”), the Fund delivers to the Designated Owners of the VRTP Shares a certificate signed by a duly authorized officer of the Fund (i) certifying that (x) the Fund has entered into corrective trades in respect of Fund Assets which upon the settlement thereof shall fully cure such Additional Mandatory Redemption Event, and (y) such corrective trades shall settle no later than the day which is twenty (20) days following such MRE Certification Date, and (ii) specifying the identity and Market Value of the Fund Assets which are the subject of such corrective trades, then the

Additional MRE Cure Date for such Additional Mandatory Redemption Event shall be extended to the twentieth (20th) day following such MRE Certification Date.

“Advances” has the meaning set forth in the Credit Agreement.

“Amendment Event” means that the Fund or the Board of Trustees shall have authorized or permitted any amendment, supplementation, modification or repeal of, or any waiver of, (i) the Statement or any provisions thereof, or (ii) the Declaration or By-Laws of the Fund or any provision thereof, (a) other than in accordance with provisions of Section 2.6 of the Statement, or (b) with respect to any other amendment, supplementation, modification, repeal, or waiver, which could reasonably be expected to give rise to a material adverse effect on any Holder or Designated Owner of the VRTP Shares.

“Credit Quality Failure” means the Fund’s failure at any time to hold at least 70% of its total assets in Assets that are rated by at least one NRSRO and are rated at least B- from S&P or at least B3 from Moody’s or any equivalent or higher rating from any other NRSRO.

“Debt” means with respect to the Fund, on any date, without duplication, (i) all “senior securities representing indebtedness” (as defined in Section 18(g) of the 1940 Act), (ii) all obligations of the Fund for borrowed money, including without limitation, all obligations of the Fund which are evidenced by letters of credit or letter of credit reimbursement agreements, (iii) all obligations of the Fund evidenced by bonds, debentures, notes, acceptances or other similar instruments, (iv) all obligations of the Fund to pay the deferred purchase price of property or services, (v) all obligations of the Fund as lessee which are capitalized in accordance with GAAP, (vi) all obligations of the Fund (that would constitute “Debt” under this definition with respect to the Fund) secured by a Lien on any asset of the Fund, whether or not such obligations are assumed by the Fund, (vii) payment obligations, fixed or contingent, under Derivative Contracts (other than covered short sales), (viii) all obligations of the Fund (that would constitute “Debt” under this definition with respect to the Fund) that are Guaranteed by the Fund, and (ix) to the extent not otherwise included, all items which in accordance with GAAP would be included in determining total liabilities as shown on the Fund’s balance sheet.

“Derivative Contract” means (a) any and all rate swap transactions, basis swaps, credit derivative transactions, forward rate transactions, commodity swaps, commodity options, forward commodity contracts, forward swap transactions, equity or equity index swaps or options, bond or bond price or bond index swaps or options or forward bond or forward bond price or forward bond index transactions, futures contracts, repurchase transactions, interest rate options, forward foreign exchange transactions, cap transactions, floor transactions, collar transactions, currency swap transactions, cross-currency rate swap transactions, currency options, spot contracts, or any other similar transactions or any combination of any of the foregoing (including any options to enter into any of the foregoing), whether or not any such transaction is governed by or subject to any master agreement or cleared on an

exchange or other clearing organization, and (b) any and all transactions of any kind, and the related confirmations, which are subject to the terms and conditions of, or governed by, any form of master agreement published by the International Swaps and Derivatives Association, Inc., any International Foreign Exchange Master Agreement, or any other master agreement (any such master agreement, together with any related schedules, a “Master Agreement”), including any such obligations or liabilities under any Master Agreement.

“Derivative Transaction Event” means the Fund’s entrance into any Derivative Contract, except for a Permitted Derivative Transaction.

“Derivatives Collateral” means Assets of the Fund which have been pledged as collateral to a counterparty to secure the Fund’s obligations to such counterparty in connection with a Permitted Derivatives Transaction.

“Derivatives Collateral Amount” means the aggregate Market Value of all of the Assets of the Fund that constitute Derivatives Collateral.

“Event of Default” has the meaning set forth in the Credit Agreement.

“Guarantee” by any Person means any obligation, contingent or otherwise, of such Person directly or indirectly guaranteeing any Debt or other obligation of any other Person and, without limiting the generality of the foregoing, any obligation, direct or indirect, contingent or otherwise, of such Person (i) to purchase or pay (or advance or supply funds for the purchase or payment of) such Debt or other obligation (whether arising by virtue of partnership arrangements, or by agreement to keep-well, to purchase assets, goods, securities or services, to take-or-pay, or to maintain financial statement conditions or otherwise), or (ii) entered into for the purpose of assuring in any other manner the obligee of such Debt or other obligation of the payment thereof or to protect such obligee against loss in respect thereof (in whole or in part), provided that the term “Guarantee” shall not include endorsements for collection or deposit in the ordinary course of business. The term “Guarantee” used as a verb has a corresponding meaning.

“Investment Policies and Restrictions” means the policies of the Fund with respect to investments, distributions, investment restrictions, tender offers, repurchases and leverage as of the date hereof (as set forth in the Offering Memorandum as of the date hereof, as such policies may be modified to the extent not giving rise to an Investment Policies Amendment Event).

“Investment Policies Amendment Event” means the Fund shall, without the consent of the Majority of Owners, (i) make or permit any change in the Investment Policies and Restrictions in effect on the date hereof, which change would be adverse to the Holders or Designated Owners of the VRTP Shares, including any change which would cause a material adverse change in the risk profile of the Fund or its Assets, unless required by a change in applicable law, or (ii) shall make or permit any change in the fundamental investment objectives, policies and restrictions (as such term is defined in the 1940 Act) of the Fund.

“Investment Policies and Restrictions Failure” means the Fund’s failure to comply in any material respect with its Investment Policies and Restrictions.

“Lien” means any mortgage, pledge, hypothecation, assignment, deposit arrangement, encumbrance, lien or security interest (statutory or other), or preference, priority or other security agreement or preferential arrangement of any kind or nature whatsoever (including, without limitation, any conditional sale or other title retention agreement, any financing lease having substantially the same economic effect as any of the foregoing, and the filing of any financing statement under the Uniform Commercial Code in effect in the State of New York or comparable law of any jurisdiction).

“Lien Failure” means the Fund’s creating, pledging, incurring or suffering to be incurred or to exist any Lien on any funds, accounts, Assets or other property of the Fund, except for Permitted Liens.

“Market Value” has the meaning set forth in the Statement.

“Permitted Derivative Transaction” means the Fund’s entrance into any Derivative Contract (other than for borrowed money) arising in the ordinary course of the Fund’s business, which is (i) permitted pursuant to the 1940 Act and the Fund’s Investment Policies and Restrictions and (ii) either (A) entered into for hedging purposes or (B) an investment in the Markit iBoxx USD Liquid Leveraged Loan Index, provided that in any case the term “Permitted Derivative Transaction” shall not include any Derivative Contract entered into by the Fund to the extent that, (i) the Derivatives Collateral Amount would exceed an amount equal to two and a quarter percent (2.25%) of the aggregate Market Value of the Fund’s total assets, (ii) the aggregate notional amount relating to investments with Derivative Contracts that constitute Permitted Derivative Transactions would exceed five percent (5%) of the Market Value of the Fund’s total assets, or (iii) to the extent such Derivatives Contract is entered into by the Fund in connection with an investment in the Markit iBoxx USD Liquid Leveraged Loan Index, the aggregate notional amount relating to all investments with Derivatives Contracts entered into by the Fund in connection with investments in the Markit iBoxx USD Liquid Leveraged Loan Index exceeds the amount of cash held by the Fund.

“Permitted Liens” means (i) Liens of any secured party created by or pursuant to the Credit Agreement, (ii) Liens of the Custodian securing overdraft extensions incurred in the ordinary course of business to the extent the aggregate amount of such overdraft extensions does not exceed $10,000,000 at any time, (iii) Liens of the Custodian which are expressly subordinated to the payment of the Fund’s obligations under the Credit Agreement, (iv) Liens for taxes, assessments or other governmental charges or levies not at the time delinquent or being diligently contested in good faith by appropriate actions and for which adequate reserves in accordance with GAAP shall have been set aside on the Fund’s books, (v) Liens in respect of judgments or awards so long as the Fund shall at the time in good faith be diligently prosecuting an appeal or proceeding for review and in respect of which a stay of execution shall have been obtained pending such appeal or review, (vi) Liens (other than non-

possessory Liens which pursuant to applicable law are, or may be, entitled to take priority (in whole or in part) over prior, perfected liens and security interests) with respect to taxes, assessments and other governmental charges or levies for amounts not yet due or which are being contested in good faith by appropriate proceedings diligently conducted and with respect to which adequate reserves have been set aside in accordance with GAAP, provided that enforcement of such Liens is stayed pending such contest, (vii) Liens in respect of fee and expense obligations to the Custodian and other similar agents which are providing services in respect of the Fund’s Assets which in each case have arisen in the ordinary course of the Fund’s business and which are not overdue for a period in excess of thirty (30) days, (viii) Liens in respect of Debt permitted under clause (iv) of the definition of “Senior Security Failure” set forth in Section 1 of this Annex, and (ix) Liens arising in connection with any Permitted Derivative Transaction.

“Permitted Refinancing Shares” means the issuance of any additional series of Preferred Shares, the proceeds of which will be used (i) to fully redeem or repurchase all outstanding VRTP Shares, or (ii) solely for the redemption or repurchase of VRTP Shares and the costs and expenses incurred in connection with the issuance of such Preferred Shares.

“Proposed Financing” as of any date of determination means any loan, financing or series of financings proposed to be provided to the Fund, including, without limitation, under any proposed credit facility, reverse repurchase facility, debt issuance facility or other financing arrangement.

“Senior Security Failure” means the Fund issuing or suffering to exist any other “senior security” (as defined in the 1940 Act as of the date hereof or, in the event such definition shall be amended, with such changes to the definition thereof as consented to by the Majority of Owners), including any Debt or Guarantee of the Fund, except (i) Debt or contingent obligations arising under the Credit Agreement, (ii) Debt in favor of the Custodian relating to Custodian’s overdraft advances incurred in the ordinary course of the Fund’s business, which are not overdue, to the extent the aggregate amount of such overdraft advances does not exceed $10,000,000 at any time, (iii) fee and expense obligations to the Custodian and other similar agents which are providing services in respect of the Fund’s Assets which in each case have arisen in the ordinary course of the Fund’s business which are not overdue for a period in excess of thirty (30) days, (iv) Debt or contingent obligations (other than Debt for borrowed money) arising in connection with transactions in the ordinary course of the Fund’s business in connection with its purchasing of securities or the entering of any Permitted Derivative Transaction, (v) obligations of the Fund to fund future extensions of credit under the Credit Agreement relating to its loan assets which do not exceed twenty percent (20%) of the aggregate Market Value of the Fund’s Assets and (vi) Debt or contingent obligations in respect of judgments or awards that have been in force for less than the applicable period for taking an appeal so long as such judgments or awards do not constitute an Event of Default under the Credit Agreement and so long as execution is not levied thereunder or in respect of which the Fund (A) shall at the time in good faith be diligently prosecuting an appeal or proceeding for review and in respect of which a stay of execution

shall have been obtained pending such appeal or review, or (B) shall have obtained an unsecured performance bond in respect of such judgment or award or (vii) the issuance of any Permitted Refinancing Shares.

Section 2. Additional Increased Rate Events

(a) In addition to the Increased Rate Events set forth in the Statement and subject to the cure provisions of Section 2(b) of this Annex, the Dividend Rate on the VRTP Shares shall be adjusted to the Increased Rate for the first day of any Increased Rate Period on which:

(1) an Amendment Event has occurred and is not cured as of a date within ten (10) Business Days after the occurrence of such event;

(2) a Credit Quality Failure has occurred and is continuing;

(3) an Investment Policies and Restrictions Failure or an Investment Policies Amendment Event has occurred and is continuing;

(4) a Senior Security Failure has occurred and is continuing;

(5) a Lien Failure has occurred and is continuing; or

(6) a Derivative Transaction Event has occurred and is continuing.

(b) No Increased Rate for the VRTP Shares shall be deemed to have commenced if (1) with respect to the Additional Increased Rate Events in clauses (2), (3), or (5) above, the Fund has cured or remedied, on or before the Additional IRE Cure Date, the failure or event giving rise to such Additional Increased Rate Event, or (2) with respect to any Additional Increased Rate Event, the Designated Owners of all Outstanding VRTP Shares have waived or affirmatively consented, in writing, to the occurrence of the failure or event giving rise to such Additional Increased Rate Event.

(c) For the avoidance of doubt, any dividends payable on VRTP Shares at the Increased Rate as a result of any Additional Increased Rate Event shall be subject to the terms and conditions of the Statement governing dividend payments, including without limitation the requirement that such dividends be paid out of Legally Available Funds.

Section 3. Additional Mandatory Redemption Events

(a) In addition to the Mandatory Redemption Events set forth in the Statement, with respect to any Additional Mandatory Redemption Event applicable to a Series of VRTP Shares, the Fund shall, not later than the close of business on the Business Day next following the last day of the cure period, if any, applicable to such Additional Mandatory Redemption Event,

cause a notice of redemption to be issued, in accordance with the terms of the VRTP Shares, for the redemption of all Outstanding VRTP Shares of such Series, at a price per VRTP Share equal to the Mandatory Redemption Price.

(b) For the avoidance of doubt, any redemption of VRTP Shares made as a result of any Additional Mandatory Redemption Event shall be subject to the terms and conditions of the Statement governing redemptions, including without limitation the requirement that such redemption be made out of Legally Available Funds.

Section 4. Amendment; Waiver

Notwithstanding anything to the contrary set forth in the Declaration, the By-Laws, the Statement or any Appendix thereto, any provision of this Annex may be amended or waived if, but only if, such amendment or waiver is in writing and is consented to in writing by the Fund and the Designated Owners of all Outstanding VRTP Shares.

Section 5. Successors and Assigns

The provisions of this Annex shall be binding upon and inure to the benefit of each of the Fund, the Purchasers and the Agent and their respective successors and assigns.

Each future Designated Owner of any VRTP Shares shall be a third-party beneficiary of this Annex and shall have the full right, power, and authority to enforce the obligations of the Fund hereunder, including without limitation, the obligations of the Fund in respect of each Additional Increased Rate Event and each Additional Mandatory Redemption Event, all as if such Designated Owner were a party to the Purchase Agreement.

NUVEEN SENIOR INCOME FUND

The undersigned, in his capacity as an officer of Nuveen Senior Income Fund (the “Fund”), hereby acknowledges and represents that the attached “ANNEX 1 TO THE PURCHASE AGREEMENT, AS AMENDED AND EFFECTIVE NOVEMBER 30, 2015” was duly authorized and adopted by the Fund.

/s/ Kevin J. McCarthy

Kevin J. McCarthy

Secretary