Exhibit 5.1

250 Vesey Street • New York, New York 10281.1047

TELEPHONE: +1.212.326.3939 • JONESDAY.COM

July 9, 2024

Great Elm Capital Corp.

3801 PGA Boulevard, Suite 603

Palm Beach Gardens, Florida 33410

Re: $22,000,000 aggregate principal amount of 8.50% Notes due 2029 of Great Elm Capital Corp.

Ladies and Gentlemen:

We have acted as counsel for Great Elm Capital Corp., a Maryland corporation (the “Company”), in connection with the issuance and sale of $22,000,000 aggregate principal amount of the Company’s 8.50% Notes due 2029 (the “Notes”), pursuant to the Purchase Agreement, dated as of July 9, 2024, entered into by and among the Company, Great Elm Capital Management, Inc., a Delaware limited liability company, and the purchasers listed on Appendix A thereto (the “Purchasers”). The Notes are being issued under a base indenture, dated as of September 18, 2017 (the “Base Indenture”), between the Company and Equiniti Trust Company, LLC, as trustee (the “Trustee”), as supplemented by the sixth supplemental indenture, dated as of April 17, 2024 (the “Sixth Supplemental Indenture”), and as further supplemented by an officers’ certificate (together with the Base Indenture and the Sixth Supplemental Indenture, the “Indenture”).

In connection with the opinion expressed herein, we have examined such documents, records and matters of law as we have deemed relevant or necessary for purposes of this opinion. Based on the foregoing, and subject to the further limitations, qualifications and assumptions set forth herein, we are of the opinion that the Notes constitute valid and binding obligations of the Company.

The opinion set forth above is subject to the following limitations, qualifications and assumptions:

For the purposes of the opinion expressed herein, we have assumed that: (i) the Trustee has authorized, executed and delivered the Indenture, (ii) the Notes have been duly authenticated by the Trustee in accordance with the terms of the Indenture and (iii) the Indenture is the valid, binding and enforceable obligation of the Trustee.

AMSTERDAM • ATLANTA • BEIJING • BOSTON • BRISBANE • BRUSSELS • CHICAGO • CLEVELAND • COLUMBUS • DALLAS DETROIT • DUBAI • DÜSSELDORF • FRANKFURT • HONG KONG • HOUSTON • IRVINE • LONDON • LOS ANGELES • MADRID MELBOURNE • MEXICO CITY • MIAMI • MILAN • MINNEAPOLIS • MUNICH • NEW YORK • PARIS • PERTH • PITTSBURGH SAN DIEGO • SAN FRANCISCO • SÃO PAULO • SHANGHAI • SILICON VALLEY • SINGAPORE • SYDNEY • TAIPEI • TOKYO • WASHINGTON

Great Elm Capital Corp. July 9, 2024 Page 2

For purposes of our opinion, we also assume that (a) the Company is a corporation existing and in good standing under the laws of the State of Maryland, (b) the Indenture and the Notes have been (i) authorized by all necessary corporate action of the Company and (ii) executed and delivered by the Company under the laws of the State of Maryland, and (c) the execution, delivery, performance and compliance with the terms and provisions of the Indenture and the Notes by the Company do not violate or conflict with the laws of the State of Maryland, the terms and provisions of the Company’s Amended and Restated Articles of Incorporation, as amended, or Bylaws, or any rule, regulation, order, decree, judgment, instrument or agreement binding upon or applicable to it or its properties.

The opinion expressed herein is limited by bankruptcy, insolvency, reorganization, fraudulent transfer and fraudulent conveyance, voidable preference, moratorium or other similar laws and related regulations and judicial doctrines from time to time in effect relating to or affecting creditors’ rights generally, and by general equitable principles and public policy considerations, whether such principles and considerations are considered in a proceeding at law or at equity.

As to facts material to the opinion and assumptions expressed herein, we have relied upon oral or written statements and representations of officers and other representatives of the Company and others. The opinion expressed herein is limited to the laws of the State of New York, as currently in effect, and we express no opinion as to the effect of the laws of any other jurisdiction.

We hereby consent to the filing of this opinion as Exhibit 5.1 to the Current Report on Form 8-K dated the date hereof filed by the Company and incorporated by reference into the Registration Statement on Form N-2 (Registration No. 333-261274) (the “Registration Statement”), filed by the Company to effect the registration of the Notes under the Securities Act of 1933 (the “Securities Act”) and to the reference to Jones Day under the caption “Legal Matters” in the prospectus constituting a part of such Registration Statement. In giving such consent, we do not thereby admit that we are included in the category of persons whose consent is required under Section 7 of the Securities Act or the rules and regulations of the Securities and Exchange Commission promulgated thereunder.

Very truly yours,

/s/ Jones Day