Exhibit 5.1

[Letterhead of Sullivan & Cromwell LLP]

October 31, 2017

The Goldman Sachs Group, Inc.,

200 West Street, New York,

New York 10282.

Ladies and Gentlemen:

We are acting as counsel to The Goldman Sachs Group, Inc., a Delaware corporation (the “Company”), in connection with the issuance and delivery, on the date hereof, of $1,250,000,000 principal amount of the Company’s Floating Rate Notes due 2022 (the “FRN due 2022”), $3,250,000,000 principal amount of the Company’s 2.876% Fixed/Floating Rate Notes due 2022 (the “2.876% Notes due 2022”), $2,500,000,000 principal amount of the Company’s 4.017% Fixed/Floating Rate Notes due 2038 (the “4.017% Notes due 2038”), and CAD750,000,000 principal amount of the Company’s 3.307% Fixed/Floating Rate Notes due 2025 (the “3.307% Notes due 2025” and, together with the FRN due 2022, the 2.876% Notes due 2022 and the 4.017% Notes due 2038, the “Notes”). The Company filed with the Securities and Exchange Commission, on July 10, 2017, a registration statement on Form S-3ASR (File No. 333-219206) (the “Registration Statement”) under the Securities Act of 1933 (the “Act”) relating to the proposed offer and sale of an unspecified principal amount of the Company’s unsecured debt securities, including the Notes. The Notes are being issued under an indenture, dated as of July 16, 2008 (as previously amended, most recently by the Fourth Supplemental Indenture, dated as of December 31, 2016, the “Indenture”), between the Company and The Bank of New York Mellon, as trustee (the “Trustee”).

In rendering this opinion, we have examined the following documents:

We also have examined such questions of law as we have considered necessary or appropriate for the purposes of this opinion. Upon the basis of such examination, it is our opinion that the Notes constitute valid and legally binding obligations of the Company, subject to bankruptcy, insolvency, fraudulent transfer, reorganization, moratorium and similar laws of general applicability relating to or affecting creditors’ rights and to general equity principles.

We note that, as of the date of this opinion, a judgment for money in an action based on securities denominated in a foreign currency (such as the 3.307% Notes due 2025) in a Federal or state court in the United States ordinarily would be enforced in the United States only in U.S. dollars. The date used to determine the rate of conversion of the foreign currency in which a particular security is denominated into U.S. dollars will depend upon various factors, including which court renders the judgment. For example, a state court in the State of New York rendering a judgment on a security denominated in a foreign currency would be required under Section 27 of the New York Judiciary Law to render such judgment in the foreign currency in which the security is denominated, and such judgment would be converted into U.S. dollars at the exchange rate prevailing on the date of entry of the judgment.

The foregoing opinion is limited to the Federal laws of the United States, the laws of the State of New York and the General Corporation Law of the State of Delaware, and we are expressing no opinion as to the effect of the laws of any other jurisdiction.

In rendering the foregoing opinion, we are not passing upon, and assume no responsibility for, any disclosure in the Registration Statement or any related prospectus or other offering material regarding the Company or the Notes or their offering and sale.

We have relied as to certain matters on information obtained from public officials, officers of the Company and other sources believed by us to be responsible, and we have assumed, without independent verification, that the Indenture has been duly authorized, executed and delivered by the Trustee, that the Notes conform to the forms thereof examined by us, that the Trustee’s certificates of authentication of the Notes have been manually signed by one of the Trustee’s authorized officers, that the Notes have been delivered against payment as contemplated in the Registration Statement and that the signatures on all documents examined by us are genuine.

We hereby consent to the filing of this opinion as an exhibit to the Registration Statement. In giving this consent, we do not thereby admit that we are in the category of persons whose consent is required under Section 7 of the Act.