Goldman Sachs Capital III S-3 Shelf registration

Exhibit 5.1

January 27, 2025

Goldman Sachs Capital VI and VII

c/o The Goldman Sachs Group, Inc.

200 West Street

New York, NY 10282

Re: Goldman Sachs Capital VI and VII

Ladies and Gentlemen:

We have acted as special Delaware counsel for Goldman Sachs Capital VI and VII, each a Delaware statutory trust (each, a “Trust” and collectively, the “Trusts”), in connection with the matters set forth herein. At your request, this opinion is being furnished to you.

For purposes of giving the opinions hereinafter set forth, our examination of documents has been limited to the examination of originals or copies of the following:

(a) The Certificate of Trust of Goldman Sachs Capital VI, as filed with the office of the Secretary of State on February 15, 2005;

(b) The Certificate of Trust of Goldman Sachs Capital VII, as filed with the office of the Secretary of State on May 3, 2017 (the documents identified in items (a) and (b) being collectively referred to as the “Certificates of Trust”);

(c) The Trust Agreement of Goldman Sachs Capital VI, dated as of February 15, 2005, between the Company and the trustee of the Trust named therein;

(d) The Trust Agreement of Goldman Sachs Capital VII, dated as of May 3, 2017, between the Company and the trustee of the Trust named therein;

(e) The Registration Statement (the “Registration Statement”) on Form S-3, relating to the Capital Securities of the Trusts representing undivided beneficial interests in the assets of the Trusts (each a “Capital Security” and collectively, the “Capital Securities”), as filed by the Company, the Trusts and others with the Securities and Exchange Commission on or about January 27, 2025;

(f) A form of Amended and Restated Trust Agreement of Goldman Sachs Capital VI, to be entered into among the Company, as depositor, the trustees of the Trust named therein, and the holders, from time to time, of undivided beneficial interests in the assets of Goldman Sachs Capital VI, incorporated by reference as an exhibit to the Registration Statement;

Goldman Sachs Capital VI and VII

January 27, 2025

Page 2

(g) A form of Amended and Restated Trust Agreement of Goldman Sachs Capital VII, to be entered into among the Company, as depositor, the trustees of the Trust named therein, and the holders, from time to time, of undivided beneficial interests in the assets of Goldman Sachs Capital VII, incorporated by reference as an exhibit to the Registration Statement (each of the documents identified in items (f) and (g) being referred to as the “Trust Agreement” and collectively as the “Trust Agreements”);

(h) A Certificate of Good Standing for Goldman Sachs Capital VI, dated January 27, 2025, obtained from the Secretary of State; and

(i) A Certificate of Good Standing for Goldman Sachs Capital VII, dated January 27, 2025, obtained from the Secretary of State.

Capitalized terms used herein and not otherwise defined are used as defined in the Trust Agreements, except that reference herein to any document shall mean such document as in effect on the date hereof.

For purposes of this opinion, we have not reviewed any documents other than the documents listed in paragraphs (a) through (i) above. In particular, we have not reviewed any document (other than the documents listed in paragraphs (a) through (i) above) that is referred to in or incorporated by reference into the documents reviewed by us. We have assumed that there exists no provision in any document that we have not reviewed that is inconsistent with the opinions stated herein. We have conducted no independent factual investigation of our own but rather have relied solely upon the foregoing documents, the statements and information set forth therein and the additional matters recited or assumed herein, all of which we have assumed to be true, complete and accurate in all material respects.

With respect to all documents examined by us, we have assumed (i) the authenticity of all documents submitted to us as authentic originals, (ii) the conformity with the originals of all documents submitted to us as copies or forms, and (iii) the genuineness of all signatures.

For purposes of this opinion, we have assumed (i) that, at the time of each issuance of the Capital Securities, the Trust Agreements and the Certificate of Trusts will be in full force and effect and will not have been amended, (ii) except to the extent provided in paragraph 1 below, the due creation or due organization or due formation, as the case may be, and valid existence in good standing of each party to the documents examined by us under the laws of the jurisdiction governing its creation, organization or formation, (iii) the legal capacity of each natural person who is a party to the documents examined by us, (iv) that each of the parties to the documents examined by us has the power and authority to execute and deliver, and to perform its obligations under, such documents, (v) the due authorization, execution and delivery by all parties thereto of all documents examined by us, (vi) that each Person to whom a Capital Security is to be issued by the Trusts (collectively, the “Capital Security Holders”) will receive appropriate Capital Securities

Goldman Sachs Capital VI and VII

January 27, 2025

Page 3

Certificates evidencing ownership of such Capital Securities and will pay for such Capital Securities acquired by it, in accordance with the Trust Agreements and the Registration Statement, and (vii) that the Capital Securities are issued and sold to the Capital Security Holders in accordance with the Trust Agreements and the Registration Statement. We have not participated in the preparation of the Registration Statement and assume no responsibility for its contents.

This opinion is limited to the laws of the State of Delaware (excluding the securities laws and blue sky laws of the State of Delaware), and we have not considered and express no opinion on the laws of any other jurisdiction, including federal laws and rules and regulations relating thereto. Our opinions are rendered only with respect to Delaware laws and rules, regulations and orders thereunder that are currently in effect.

Based upon the foregoing, and upon our examination of such questions of law and statutes of the State of Delaware as we have considered necessary or appropriate, and subject to the assumptions, qualifications, limitations and exceptions set forth herein, we are of the opinion that:

1. Each Trust has been duly formed and is validly existing in good standing as a statutory trust under the Delaware Statutory Trust Act (12 Del. C. § 3801, et seq.).

2. The Capital Securities will represent valid and, subject to the qualifications set forth in paragraph 3 below, fully paid and nonassessable undivided beneficial interests in the assets of its respective Trust.

3. The Capital Security Holders, as beneficial owners of the Trusts, will be entitled to the same limitation of personal liability extended to stockholders of private corporations for profit organized under the General Corporation Law of the State of Delaware. We note that the Capital Security Holders may be obligated to make payments as set forth in the Trust Agreements.

We consent to the filing of this opinion with the Securities and Exchange Commission as an exhibit to the Registration Statement. In addition, we hereby consent to the use of our name under the heading “Validity of Securities” in the Prospectus. In giving the foregoing consents, we do not thereby admit that we come within the category of Persons whose consent is required under Section 7 of the Securities Act of 1933, as amended, or the rules and regulations of the Securities and Exchange Commission thereunder. Except as stated above, without our prior written consent, this opinion may not be furnished or quoted to, or relied upon by, any other Person for any purpose.

Very truly yours,

/s/ Richards, Layton & Finger, P.A.

JWP/KNR