Exhibit 5.1

One International Place,
40th Floor
100 Oliver Street
Boston, MA  02110-2605 +1  617  728  7100  Main +1  617  426  6567  Faxwww.dechert.com

September 4, 2025

Horizon Technology Finance Corporation
312 Farmington Avenue
Farmington, Connecticut 06032

Re:         Registration Statement on Form N-2

Ladies and Gentlemen:

We have acted as counsel to Horizon Technology Finance Corporation, a Delaware corporation (the “Company”), in connection with the preparation and filing of a registration statement on Form N-2 (File No. 333-278396) as originally filed on June 6, 2024 and declared effective by the U.S. Securities and Exchange Commission (the “Commission”) on June 20, 2024 under the Securities Act of 1933, as amended (the “Securities Act”) (such registration statement, as amended, including the exhibits and schedules thereto, at its most recent effective date, and including any information contained in the Prospectus (as defined below) subsequently filed with the Commission pursuant to Rule 424 or deemed to be part of such registration statement pursuant to Rule 430B of the Commission under the Securities Act and any information incorporated by reference into any of the foregoing, being referred to collectively as the “Registration Statement”), relating to the public offering of securities of the Company that may be offered by the Company from time to time as set forth in the prospectus dated June 20, 2024 (the “Prospectus”), which formed a part of the Registration Statement at the time it became effective, and as may be set forth from time to time in amounts, at prices, and on terms to be set forth in one or more supplements to the Prospectus. This opinion letter is rendered in connection with (i) the issuance and sale by the Company of $40,000,000 aggregate principal amount of the Company’s 5.50% Convertible Notes due 2030 (the “Notes”) and (ii) the authorization and reservation for issuance of shares of the Company’s common stock, par value $0.001 per share, issuable upon the conversion of the Notes at the then-existing conversion rate (the “Conversion Shares”) by the holders thereof, as described in the prospectus supplement dated September 4, 2025 (the “Prospectus Supplement”), filed with the Commission pursuant to Rule 424 under the Securities Act. All of the Notes are to be sold by the Company as described in the Registration Statement and related Prospectus and Prospectus Supplement. This opinion letter is being furnished to the Company in accordance with the requirements of Item 25 of Form N-2 under the Investment Company Act of 1940, as amended (the “1940 Act”), and we express no opinion herein as to any matter other than as to the legality of the Purchase Agreement (as defined below), the Notes and the Conversion Shares.

September 4, 2025 Page 2

The Notes are to be issued pursuant to the purchase agreement dated as of September 4, 2025 (the “Purchase Agreement”), among the Company and several purchasers set forth on Schedule A attached thereto (collectively, the “Purchasers”).

In rendering the opinions expressed below, we have examined and relied on originals or copies, certified or otherwise identified to our satisfaction, of such documents, corporate records and other instruments and such agreements, certificates and receipts of public officials, certificates of officers or other representatives of the Company and others, and such other documents as we have deemed necessary or appropriate as a basis for the opinions set forth below, including the following documents:

(i) the Registration Statement;

(ii) the Purchase Agreement;

(iii) the Amended and Restated Certificate of Incorporation of the Company;

(iv) the Amended and Restated Bylaws of the Company;

(v) a certificate of good standing with respect to the Company issued by the Secretary of State of the State of Delaware as of a recent date; and

(vi) resolutions of the board of directors of the Company relating to, among other things, the authorization and issuance of the Notes and the Conversion Shares.

As to the facts upon which this opinion is based, we have relied, to the extent we deem proper, upon certificates of public officials (which we have assumed remain accurate as of the date of this opinion letter) and certificates and written statements of agents, officers, directors and representatives of the Company without having independently verified such factual matters.

In our examination, we have assumed the genuineness of all signatures, the authenticity of all documents submitted to us as original documents, the conformity to original documents of all documents submitted to us as copies, the legal capacity of natural persons who are signatories to the documents examined by us, and the legal power and authority of all persons signing on behalf of the parties to such documents (other than the Company). We have further assumed that there has been no oral modification of, or amendment or supplement (including any express or implied waiver, however arising) to, any of the agreements, documents or instruments used by us to form the basis of the opinion expressed below.

September 4, 2025 Page 3

On the basis of the foregoing and subject to the assumptions, qualifications and limitations set forth in this letter, we are of the opinion that:

1.         The Purchase Agreement has been duly authorized, executed and delivered by the Company and constitutes the valid and legally binding obligation of the Company, enforceable against the Company in accordance with its terms.

2.         When the Purchase Agreement is duly executed by the Company and when the Notes are issued pursuant to, and in accordance with the terms set forth in, the Purchase Agreement, the Notes will constitute valid and legally binding obligations of the Company, enforceable against the Company in accordance with their terms.

3.         The Conversion Shares have been duly authorized and, when issued upon conversion of the Notes pursuant to, and in accordance with the terms set forth in, the Purchase Agreement and countersigned, if required, by the transfer agent therefor, will be validly issued, fully paid and nonassessable.

The opinions set forth herein are subject to the following assumptions, qualifications, limitations and exceptions being true and correct at or before the issuance of the Notes:

(i) the Purchase Agreement has been duly authorized, executed and delivered by each party thereto (other than the Company); and

(ii) the terms of the Notes as established comply with the applicable requirements of the 1940 Act.

The foregoing opinions are subject to the following qualifications:

(a)         The opinions expressed herein are limited by principles of equity (regardless of whether considered in a proceeding in equity or at law) that may limit the availability of certain rights and remedies and do not reflect the effect of bankruptcy (including preferences), insolvency, reorganization, fraudulent conveyance, receivership, reorganization, moratorium and other laws or decisions relating to or affecting debtors’ obligations or creditors’ rights generally and, as to rights of indemnification and contribution, by principles of public policy. The opinions expressed above also do not reflect the effect of laws and equitable doctrines (including requirements that the parties to agreements act reasonably and in good faith and in a commercially reasonable manner, and give reasonable notice prior to exercising rights and remedies) or the effect of the exercise of discretion of the court before which any proceeding may be brought, which may limit the availability of any particular remedy but which will not, in our judgment, make the remedies available to the Purchasers under the Purchase Agreement, taken as a whole, inadequate for the practical realization of the benefits provided for in the Purchase Agreement, except for the economic consequence of any delay that may be imposed thereby or result therefrom, and except that we express no opinion as to the rights of the Purchasers to accelerate the due dates of any payment due under the Purchase Agreement or the Notes or to exercise other remedies available to them on the happening of a non-material breach of any such document or agreement.

September 4, 2025 Page 4

(b)         Without limiting the generality of the foregoing, we express no opinion with respect to: (1) the availability of specific performance or other equitable remedies for noncompliance with any of the provisions contained in the Purchase Agreement; (2) the enforceability of provisions contained in the Purchase Agreement relating to the effect of laws which may be enacted in the future; (3) the enforceability of provisions in the Purchase Agreement purporting to waive the effect of applicable laws to the extent such waivers are prohibited by such applicable laws; (4) the effectiveness of any power-of-attorney given under the Purchase Agreement that is intended to bind successors and assigns that have not granted such powers by a power-of-attorney specifically executed by them; (5) provisions in the Purchase Agreement related to waivers of remedies (or the delay or omission of enforcement thereof), disclaimers, liability limitations or limitations on the obligations of the Purchasers in circumstances in which a failure of condition or default by any party is not material; (6) the indemnification and contribution provisions of the Purchase Agreement if and to the extent that such provisions contravene public policy or might require indemnification or payments with respect to any litigation against a party to the Purchase Agreement determined adversely to the other party(ies) to such litigation, or any loss, cost or expense arising out of an indemnified party’s bad faith, gross negligence or willful misconduct or any violation by an indemnified party of statutory duties, general principles of equity or public policy; (7) any self-help provisions in the Purchase Agreement; (8) provisions in the Purchase Agreement that purport to establish evidentiary standards; (9) provisions in the Purchase Agreement that provide that certain rights or obligations are absolute or unconditional (other than guarantees or letter of credit reimbursement obligations); (10) provisions in the Purchase Agreement that provide for the enforceability of the remaining terms and provisions of the Purchase Agreement in circumstances in which certain other terms and provisions of the Purchase Agreement are illegal or unenforceable; (11) provisions in the Purchase Agreement that restrict access to or waive legal or equitable remedies or access to courts; (12) provisions in the Purchase Agreement that affect or confer jurisdiction (other than on the courts of New York); (13) provisions in the Purchase Agreement that permit each Purchaser to act in its sole discretion or to be exculpated from liability for its actions to the extent not permitted by law; (14) any provision of the Purchase Agreement that may be construed as a forfeiture or penalty; (15) any provision of the Purchase Agreement that purports to provide that the terms thereof may not be varied or waived except in writing or that the express terms thereof supersede any inconsistent course of performance and/or usage of the trade; or (16) the effect of the laws of any jurisdiction in which a holder of the Notes is located that limits the interest, fees or other charges it may impose for the Notes or use of money or other credit.

We are members of the bar of the State of New York, and the foregoing opinions are limited to the federal laws of the United States of America, the laws of the State of New York and the General Corporation Law of the State of Delaware. We express no opinion concerning the laws of any other jurisdiction, and we express no opinion concerning any state securities or “blue sky” laws, rules or regulations, or any federal, state, local or foreign laws, rules or regulations.

September 4, 2025 Page 5

This opinion letter has been prepared for the Company’s use solely in connection with the Registration Statement. The opinions expressed in this opinion letter (i) are strictly limited to the matters stated in this opinion letter, and without limiting the foregoing, no other opinions are to be implied and (ii) are only as of the date of this opinion letter, and we are under no obligation, and do not undertake, to advise the addressee of this opinion letter or any other person or entity either of any change of law or fact that occurs, or of any fact that comes to our attention, after the date of this opinion letter, even though such change or such fact may affect the legal analysis or a legal conclusion in this opinion letter.

We hereby consent to the filing of this opinion letter as an exhibit to the Company’s Current Report on Form 8-K filed with the Commission on September 4, 2025 and to the reference to this firm under the caption “Legal Matters” in the prospectus that is a part of the Registration Statement and the Prospectus Supplement. In giving such consent, we do not admit that we are in the category of persons whose consent is required under Section 7 of the Securities Act or the rules and regulations of the Commission thereunder.

Very truly yours,

/s/ Dechert LLP

Dechert LLP