Exhibit (a)(1)(E)

This announcement is neither an offer to purchase nor a solicitation of an offer to sell Shares (as defined below). The Offer (as defined below) is made solely pursuant to the Offer to Purchase, dated November 29, 2021, and the related Letter of Transmittal, and any amendments or supplements to such Offer to Purchase or Letter of Transmittal. Purchaser (as defined below) is not aware of any state where the making of the Offer is prohibited by any administrative or judicial action pursuant to any valid state statute. If Purchaser becomes aware of any valid state statute prohibiting the making of the Offer or the acceptance of the Shares pursuant thereto, Purchaser will make a good faith effort to comply with that state statute or seek to have such statute declared inapplicable to the Offer. If, after a good faith effort, Purchaser cannot do so, Purchaser will not make the Offer to the holders of Shares in that state. Except as set forth above, the Offer is being made to all holders of Shares. In any jurisdiction where the securities, “blue sky” or other laws require the Offer to be made by a licensed broker or dealer, the Offer will be deemed to be made on behalf of Purchaser by one or more registered brokers or dealers that are licensed under the laws of such jurisdiction.

Notice of Offer to Purchase for Cash

All Outstanding Shares of Common Stock

of

CoreSite Realty Corporation

at

$170.00 Per Share

by

Appleseed Merger Sub LLC

a wholly owned direct subsidiary of

Appleseed Holdco LLC

and a wholly owned indirect subsidiary of

American Tower Investments LLC

and a wholly owned indirect subsidiary of

American Tower Corporation

Appleseed Merger Sub LLC, a Maryland limited liability company (“Purchaser”), a wholly owned direct subsidiary of Appleseed Holdco LLC, a Delaware limited liability company (“Holdco”), and a wholly owned indirect subsidiary American Tower Investments LLC, a California limited liability company (“Parent”), and a wholly owned indirect subsidiary of American Tower Corporation, a Delaware corporation (“ATC”), is offering to purchase all outstanding shares of common stock, par value $0.01 per share (the “Shares”) of CoreSite Realty Corporation, a Maryland corporation (“CoreSite”), at a price of $170.00 per Share (the “Offer Price”) without interest and subject to any applicable withholding taxes, net to the seller in cash, upon the terms and subject to the conditions set forth in the Offer to Purchase, dated November 29, 2021 (as it may be amended or supplemented from time to time, the “Offer to Purchase”), and in the related Letter of Transmittal (as it may be amended from time to time and, together with the Offer to Purchase, the “Offer”).

The Offer is being made in connection with the Agreement and Plan of Merger, dated as of November 14, 2021, among Parent, Holdco, Purchaser, Appleseed OP Merger Sub LLC, a Delaware limited liability company (“OP Merger Sub”), CoreSite, CoreSite, L.P., a Delaware limited partnership (the “OP”) and ATC (as it may be amended from time to time, the “Merger Agreement”), under which, after the completion of the Offer and the satisfaction or waiver of certain conditions, (i) Purchaser will be merged with and into CoreSite, without a vote of CoreSite stockholders in accordance with Section 3-106.1 of the Maryland General Corporation Law (the “MGCL”), and CoreSite will be the surviving corporation and a wholly owned subsidiary of Holdco (such corporation, the “Interim Surviving Entity” and such merger, the “REIT Merger”), (ii) substantially concurrently with the REIT Merger, OP Merger Sub will merge with and into the OP, with the OP continuing as the surviving limited partnership (the “OP Merger”) and (iii) immediately following the REIT Merger and the OP Merger, the Interim Surviving Entity will merge with and into Holdco, with Holdco continuing as the surviving limited liability company (such limited liability company, the “Surviving Entity”, and such merger, the “Holdco Merger”, and together with the REIT Merger and the OP Merger, the “Mergers”). At the effective time of the

REIT Merger, and as a result of the REIT Merger, CoreSite will cease to be a publicly traded company and each Share issued and outstanding immediately prior to such time (other than (i) certain restricted Shares and (ii) Shares held by Parent, Holdco, Purchaser or OP Merger Sub), will be converted into the right to receive an amount in cash equal to the Offer Price. At the effective time of the OP Merger, each partnership unit issued and outstanding and held by a limited partner of the OP (excluding CoreSite) will be converted into the right to receive an amount in cash equal to the Offer Price. Under no circumstances will interest be paid on the purchase price for Shares, regardless of any extension of the Offer or any delay in making payment for Shares. The parties to the Merger Agreement have agreed that, upon the terms and subject to the conditions specified in the Merger Agreement, the REIT Merger will be effected following the consummation of the Offer in accordance with Section 3-106.1 of the MGCL, and a vote of the CoreSite stockholders will not be required. Accordingly, if the Offer is consummated, Purchaser will not seek the approval of CoreSite’s remaining public stockholders before effecting the REIT Merger. The Merger Agreement is more fully described in the Offer to Purchase.

Tendering stockholders who have Shares registered in their names and who tender directly to American Stock Transfer & Trust Company, LLC (the “Depositary”) will not be obligated to pay brokerage fees or commissions or, except as set forth in the Letter of Transmittal, transfer taxes on the purchase of Shares by Purchaser pursuant to the Offer. Stockholders who hold their Shares through a broker or bank should consult with such institution as to whether it charges any service fees or commissions.

THE OFFER AND WITHDRAWAL RIGHTS WILL EXPIRE AT ONE MINUTE AFTER 11:59 P.M., EASTERN TIME, ON DECEMBER 27, 2021 (SUCH DATE, OR ANY SUBSEQUENT DATE TO WHICH THE EXPIRATION OF THE OFFER IS EXTENDED, THE “EXPIRATION DATE”), UNLESS THE OFFER IS EXTENDED OR EARLIER TERMINATED.

The Offer is conditioned upon, (i) there having been validly tendered in the Offer and not validly withdrawn immediately prior to one minute after 11:59 P.M., Eastern time, on the Expiration Date, a number of Shares that, considered together with all Shares (if any) beneficially owned by Parent or any of its wholly owned subsidiaries, represents at least a majority of all Shares outstanding at the time the Offer expires (the “Minimum Tender Condition”), (ii) the absence of, since the date of the Merger Agreement, any Company Material Adverse Effect (as defined in the Offer to Purchase) or any event, change or effect that, individually in the aggregate, would reasonably be expected to have, a Company Material Adverse Effect, (iii) Parent having received a written opinion of CoreSite’s regular REIT tax counsel (or if such counsel is unable to issue such opinion, such other counsel reasonably acceptable to Parent), dated as of the closing date of the Mergers, in a form reasonably agreed to by Parent, to the effect that CoreSite has, since its taxable year ended on December 31, 2016 and through the consummation of the Holdco Merger, been organized and operated in conformity with the requirements for qualification and taxation as a real estate investment trust within the meaning of Section 856 through 860 of the Internal Revenue Code of 1986, as amended (the “Code”), under the Code, subject to customary exceptions, assumptions and qualifications and based on representations contained in a tax representation letter delivered by CoreSite to such counsel and (iv) the satisfaction of other customary conditions as described in Section 13 of the Offer to Purchase. There is no financing condition to the Offer.

At a meeting of the CoreSite board of directors held on November 14, 2021, the CoreSite board of directors unanimously (i) determined that the Merger Agreement, and the transactions contemplated thereby, including the Offer and the Mergers are advisable, and in the best interests of CoreSite, (ii) duly and validly authorized and approved, and declared advisable, the execution, delivery and performance of the Merger Agreement and the consummation of the REIT Merger and the other transactions contemplated by the Merger Agreement, and (iii) resolved to recommend that the CoreSite stockholders accept the Offer and tender their Shares pursuant to the Offer.

CoreSite will file a Solicitation/Recommendation Statement on Schedule 14D-9 (the “Schedule 14D-9”) with the United States Securities and Exchange Commission (the “SEC”) and disseminate the Schedule 14D-9 to CoreSite stockholders with the Offer to Purchase. The Schedule 14D-9 will include a description of the CoreSite board of directors’ reasons for authorizing and approving the Merger Agreement, the Mergers and the transactions contemplated thereby and therefore stockholders are encouraged to review the Schedule 14D-9 carefully and in its entirety.

The Merger Agreement contains provisions to govern the circumstances in which Purchaser is permitted or required to extend the Offer. Specifically, (i) if at any then-scheduled expiration date, any condition to the Offer (other than the Minimum Tender Condition) is not satisfied and has not been waived (to the extent waivable by Purchaser), Purchaser will extend the offer for additional periods of up to ten business days per extension (except as described below) in order to permit such condition to be satisfied, (ii) if at any then-scheduled expiration date each condition to the Offer (other than the Minimum Tender Condition) is satisfied or has been waived by Purchaser (to the extent waivable by Purchaser), then Purchaser may, and upon CoreSite’s request, must, extend the Offer for additional periods of up to ten business days per extension (except as described below) in order to permit the Minimum Tender Condition to be satisfied (provided that Purchaser cannot be required by CoreSite to extend the expiration date more than three times), (iii) Purchaser will extend the Offer for the minimum period required by any law or rules, regulations, interpretations or positions of the SEC or its staff or the New York Stock Exchange (including in order to comply with Exchange Act Rule 14e-1(b) in respect of any change in the Offer Price, and (iv) Purchaser may extend the Offer for any period necessary to satisfy the requirements contained in Section 3-106(e)(1) of the MGCL. In each case described above, the Offer may be extended until (unless otherwise agreed by Purchaser and CoreSite) the earliest of (a) the termination of the Merger Agreement in accordance with its terms, (b) May 13, 2022 and (c) the final expiration date following extension of the Offer in compliance with the terms of the Merger Agreement. Furthermore, the parties to the Merger Agreement have agreed that the Offer may not expire during the period between December 30, 2021 and January 14, 2022, and in the event the terms of the Merger Agreement would permit or require Purchaser to extend the Expiration Date to a date during such period, Purchaser may or must instead extend the Offer to the first business day after January 14, 2022.

The purpose of the Offer and the Mergers is for ATC and its affiliates, through Purchaser, to acquire control of, and the entire equity interest in, CoreSite. Following the consummation of the Offer, subject to the satisfaction or waiver of the conditions set forth in the Merger Agreement, ATC, Parent, Holdco and Purchaser intend to effect the Mergers. Pursuant to the Merger Agreement, MGCL 3-202 and the charter of CoreSite, no appraisal rights or rights of an objecting stockholder are available to CoreSite stockholders in connection with the Offer or the REIT Merger

Purchaser expressly reserves the right to (i) waive or modify (to the extent permitted under applicable law) any condition to the Offer, (ii) increase the amount of cash constituting the Offer Price and (iii) make any other changes in the terms and conditions of the Offer that are not inconsistent with the terms of the Merger Agreement, except that CoreSite’s prior written approval is required for Purchaser to: (a) decrease the Offer Price, (b) change the form of consideration payable in the Offer (except that Purchaser may increase the cash consideration payable in the Offer), (c) decrease the number of Shares sought to be purchased in the Offer, (d) impose conditions or requirements to the Offer in addition to the conditions described in Section 13 of the Offer to Purchaser, (e) amend or waive the Minimum Tender Condition, (f) otherwise amend or modify any of the other terms of the Offer in a manner that adversely affects the holders of Shares or would, individually or in the aggregate, reasonably be expected to prevent or materially delay the consummation of the Offer or impair the ability of Parent, Holdco, Purchaser or OP Merger Sub to consummate the Offer or the Mergers, (g) terminate the Offer or accelerate, extend or otherwise change the Expiration Date except as provided in the Merger Agreement or (h) provide any “subsequent offering period” within the meaning of Rule 14d-11 under the Securities Exchange Act of 1934, as amended.

Any extension, waiver or amendment of the Offer or termination of the Offer will be followed, as promptly as practicable, by public announcement thereof, such announcement in the case of an extension to be issued no later than 9:00 a.m., Eastern Time, on the next business day after the previously scheduled Expiration Date.

For purposes of the Offer, Purchaser will be deemed to have accepted for payment, and thereby purchased, Shares validly tendered, and not properly withdrawn, prior to the expiration of the Offer if and when Purchaser gives oral or written notice to the Depositary of Purchaser’s acceptance for payment of such Shares pursuant to the Offer. Upon the terms and subject to the conditions of the Offer, payment for Shares accepted for payment pursuant to the Offer will be made by deposit of the aggregate Offer Price for such Shares with the Depositary, which will act as paying agent for the tendering stockholders for the purpose of receiving payments from

Purchaser and transmitting such payments to the tendering stockholders. Under no circumstances will interest be paid on the Offer Price for Shares, regardless of any extension of the Offer or any delay in making payment for Shares.

In all cases, payment for Shares tendered and accepted for payment pursuant to the Offer will be made only after timely receipt by the Depositary of (a) certificates for such Shares (“Share Certificates”) or timely confirmation of the book-entry transfer of such Shares (“Book-Entry Confirmations”) into the Depositary’s account at The Depository Trust Company (“DTC”) pursuant to the procedures set forth in the Offer to Purchase, (b) a Letter of Transmittal, properly completed and duly executed, with any required signature guarantees (or, in the case of a book-entry transfer, an Agent’s Message (as defined in the Offer to Purchase) in lieu of the Letter of Transmittal) and (c) any other documents required by the Letter of Transmittal. Accordingly, tendering stockholders may be paid at different times depending upon when Share Certificates or Book-Entry Confirmations with respect to Shares are actually received by the Depositary.

Pursuant to Section 14(d)(5) of the Securities Exchange Act of 1934, as amended, Shares tendered pursuant to the Offer may be withdrawn at any time prior to the expiration of the Offer and, unless theretofore accepted for payment by Purchaser pursuant to the Offer, may also be withdrawn at any time after January 28, 2022, which is the 60th day after the date of the commencement of the Offer.

For a withdrawal of Shares to be effective, a written notice of withdrawal must be timely received by the Depositary at its address set forth on the back cover of the Offer to Purchase. Any such notice of withdrawal must specify the name of the person having tendered the Shares to be withdrawn, the number of Shares to be withdrawn and the name of the record holder of the Shares to be withdrawn, if different from that of the person who tendered such Shares. The signature(s) on the notice of withdrawal must be guaranteed by an Eligible Institution (as defined in the Offer to Purchase), unless such Shares have been tendered for the account of any Eligible Institution. If Shares have been tendered pursuant to the procedures for book-entry transfer as set forth in the Offer to Purchase, any notice of withdrawal must specify the name and number of the account at DTC to be credited with the withdrawn Shares and must otherwise comply with DTC’s procedures. If certificates representing the Shares to be withdrawn have been delivered or otherwise identified to the Depositary, the name of the registered holder and the serial numbers shown on such certificates must also be furnished to the Depositary as aforesaid prior to the physical release of such certificates.

All questions as to the form and validity (including time of receipt) of any notice of withdrawal will be determined by Purchaser, in its sole discretion, which determination shall be final and binding, subject to the rights of tendering stockholders to challenge Purchaser’s determination in a court of competent jurisdiction. No withdrawal of tendered Shares shall be deemed to have been properly made until all defects and irregularities have been cured or waived. None of ATC, Parent, Holdco or Purchaser or any of their respective affiliates or assigns, the Depositary, the Information Agent (listed below), or any other person will be under any duty to give notification of any defects or irregularities in any notice of withdrawal or incur any liability for failure to give such notification. Withdrawals of tendered Shares may not be rescinded, and any Shares properly withdrawn will be deemed not to have been validly tendered for purposes of the Offer. However, withdrawn Shares may be retendered by following one of the procedures for tendering Shares described in the Offer to Purchase at any time prior to the expiration of the Offer.

The information required to be disclosed by paragraph (d)(1) of Rule 14d-6 under the Securities and Exchange Act of 1934, as amended, is contained in the Offer to Purchase and is incorporated herein by reference.

CoreSite has provided Purchaser with its stockholder list and securities position listings for the purpose of disseminating to the holders of Shares information regarding the Offer. The Offer to Purchase and related Letter of Transmittal will be mailed to record holders of Shares whose names appear on CoreSite’s stockholder list and will be furnished to brokers, dealers, commercial banks, trust companies and similar persons whose names, or the names of whose nominees, appear on the stockholder list or, if applicable, who are listed as participants in a clearing agency’s security position listing for subsequent transmittal to beneficial owners of Shares.

The receipt of the Offer Price for Shares in the Offer or consideration for Shares in the REIT Merger will generally be a taxable transaction for U.S. federal income tax purposes. Stockholders should consult with their tax advisors as to the particular tax consequences of the Offer and the REIT Merger to them. For a more complete description of material U.S. federal income tax consequences of the Offer and the REIT Merger, see the Offer to Purchase.

The Offer to Purchase, the related Letter of Transmittal and CoreSite’s Solicitation/Recommendation Statement on Schedule 14D-9 (which contains the recommendation of the CoreSite board of directors and the reasons therefor) contain important information and should be read carefully and in their entirety before any decision is made with respect to the Offer.

Questions and requests for assistance may be directed to the Information Agent at the address and telephone numbers set forth below. Requests for copies of the Offer to Purchase and the related Letter of Transmittal and other tender offer materials may be directed to the Information Agent or to brokers, dealers, commercial banks or trust companies. Such copies will be furnished promptly at Purchaser’s expense. Except as set forth in the Offer to Purchase, none of ATC, Parent, Holdco or Purchaser will pay any fees or commissions to any broker or dealer or any other person for soliciting tenders of Shares pursuant to the Offer.

The Information Agent for the Offer is:

Innisfree M&A Incorporated

501 Madison Avenue, 20th Floor

New York, New York 10022

Stockholders may call toll free: (877) 717-3904

Banks and Brokers may call collect: (212) 750-5833

November 29, 2021