Exhibit 5.1

February 11, 2020

Goldman Sachs BDC, Inc.

200 West Street

New York, New York 10282

Ladies and Gentlemen:

We have acted as counsel to Goldman Sachs BDC, Inc., a Delaware corporation (the “Company”), in connection with the Company’s (i) Registration Statement on Form N-2 (Registration No. 333-230801) filed with the Securities and Exchange Commission (the “Commission”) under the Securities Act of 1933, as amended (the “Securities Act”) (as amended from time to time, the “Initial Registration Statement”) and (ii) an additional Registration Statement on Form N-2 (Registration No. 333-236303) filed pursuant to Rule 462(b) under the Securities Act (the “462(b) Registration Statement” and, together with the Initial Registration Statement, the “Registration Statement”).

This opinion letter is rendered in connection with the issuance and sale by the Company of $360,000,000 aggregate principal amount of the Company’s 3.750% Notes due 2025 (the “Notes”), as described in the prospectus, dated as of February 6, 2020, filed with the Commission pursuant to Rule 497 under the Securities Act (the “Prospectus”). The Notes are being sold by the Company pursuant to an underwriting agreement, dated as of February 6, 2020, by and among the Company, Goldman Sachs Asset Management L.P. and BofA Securities, Inc., as representative of the several underwriters named therein (the “Underwriting Agreement”). The Notes were issued pursuant to a base indenture dated as of February 10, 2020 (the “Base Indenture”) between the Company and Wells Fargo Bank, National Association, as trustee (the “Trustee”), as supplemented by a first supplemental indenture dated as of February 10, 2020 (together with the Base Indenture, the “Indenture”), between the Company and the Trustee.

With your permission, all assumptions and statements of reliance herein have been made without any independent investigation or verification on our part, and we express no opinion with respect to the subject matter or accuracy of such assumptions or items relied upon.

In connection with this opinion, we have (i) investigated such questions of law, (ii) examined originals or certified, conformed, electronic or reproduction copies of such agreements, instruments, documents and records of the Company, such certificates of public officials and such other documents, and (iii) received such information from officers and representatives of the Company as we have deemed necessary or appropriate for the purposes of this opinion. We have examined, among other documents, the following:

The documents referred to in items (c) through (e), inclusive, are referred to collectively herein as the “Documents.”

In all such examinations, we have assumed the legal capacity of all natural persons, the genuineness of all signatures, the authenticity of original and certified documents and the conformity to original or certified documents of all copies submitted to us as certified, conformed, electronic or reproduction copies. As to various questions of fact relevant to the opinion expressed herein, we have relied upon, and assume the accuracy of, certificates and oral or written statements and other information of or from public officials and officers and representatives of the Company and others.

To the extent it may be relevant to the opinion expressed below, we have assumed that (i) the Notes have been duly authenticated, executed and delivered by the Trustee, (ii) all of the parties to the Documents (other than the Company) are validly existing and in good standing under the laws of their respective jurisdictions of organization, (iii) all of the parties to the Documents (other than the Company) have the power and authority to (a) execute and deliver the Documents, (b) perform their obligations thereunder, and (c) consummate the transactions contemplated thereby, (iv) each of the Documents has been duly authorized, executed and delivered by each of the parties thereto (other than the Company), (v) each of the Documents constitutes a valid and binding obligation of each of the parties thereto (other than as expressly addressed in the opinion below as to the Company), enforceable against such parties in accordance with their respective terms, and (vi) all of the parties to the Documents will comply with all of their obligations under the Documents and all laws applicable thereto.

Based upon the foregoing and subject to the limitations, qualifications and assumptions set forth herein, we are of the opinion that the Notes constitute valid and binding obligations of the Company, enforceable against the Company in accordance with their terms and entitled to the benefits of the Indenture.

We express no opinion as to the validity or binding effect of any provision of the Documents:

(i) relating to indemnification, contribution or exculpation;

(ii) containing any purported waiver, release, variation, disclaimer, consent or other agreement of similar effect (all of the foregoing, collectively, a “Waiver”) by any party under any provision of the Documents to the extent limited by provisions of applicable law (including judicial decisions), or to the extent that such a Waiver applies to a right, claim, duty, defense or ground for discharge otherwise existing or occurring as a matter of law (including judicial decisions), except to the extent that such a Waiver is effective under, and is not prohibited by or void or invalid under, provisions of applicable law (including judicial decisions);

(iii) related to (a) forum selection or submission to jurisdiction (including, without limitation, any waiver of any objection to venue in any court or of any objection that a court is an inconvenient forum) to the extent that the validity or binding effect of any such provision is to be determined by any court other than a court of the State of New York, (b) choice of governing law to the extent that the validity or binding effect of any such provision is to be determined by any court other than a court of the State of New York or a federal district court sitting in the State of New York, in each case, applying the choice of law principles of the State of New York, (c) service of process or (d) waiver of any rights to trial by jury;

(iv) specifying that provisions thereof may be waived only in writing;

(v) that purports to create a trust or other fiduciary relationship or a power of attorney;

(vi) specifying that any person may exercise set-off or similar rights other than in accordance with applicable law;

(vii) relating to payment of late charges, interest (or discount or equivalent amounts), premium, “make-whole” payments, collection costs or fees at a rate or in an amount, after or upon the maturity or acceleration of the liabilities evidenced or secured thereby or after or during the continuance of any default or other circumstance, or upon prepayment, that a court would determine in the circumstances to be unreasonable, a penalty or a forfeiture;

(viii) purporting to give any person or entity the power to accelerate obligations without any notice to the obligor; and

(ix) which may be construed to be in the nature of a penalty.

We express no opinion as to the validity or binding effect of any provision of the Documents (i) providing for payments thereunder in a currency other than currency of the United States of America to the extent that a court of competent jurisdiction, under applicable law, will convert any judgment rendered in such other currency into currency of the United States of America or to the extent that payment in a currency other than currency of the United States of America is contrary to applicable law, (ii) providing for governmental authority to limit, delay or prohibit the making of payments outside the United States or in foreign currency or composite currency or (iii) concerning the enforceability of the waiver of rights or defenses contained in the Documents relating to waiver of stay, extension or usury laws.

The opinion set forth above is subject to the following qualifications: (i) applicable bankruptcy, insolvency, reorganization, moratorium and other similar laws (or related judicial doctrines) now or hereafter in effect affecting creditors’ rights and remedies generally, (ii) general principles of equity including, without limitation, standards of materiality, good faith, fair dealing and reasonableness, equitable defenses and limits as to the availability of equitable remedies, whether such principles are considered in a proceeding at law or in equity, and (iii) the application of any applicable fraudulent conveyance, fraudulent transfer, fraudulent obligation, or preferential transfer law or any law governing the distribution of assets of any person now or hereafter in effect affecting creditors’ rights and remedies generally.

The opinion expressed herein is limited to the laws of the State of New York and the applicable provisions of the General Corporation Law of the State of Delaware, each as currently in effect, and no opinion is expressed with respect to any other laws or any effect that such other laws may have on the opinion expressed herein. The opinion expressed herein is limited to the matters stated herein, and no opinion is implied or may be inferred beyond the matters expressly stated herein. This letter is given only as of the time of its delivery, and we undertake no responsibility to update or supplement this letter after its delivery.

We hereby consent to the filing of this opinion as an exhibit to the Company’s Form 8-K, which will be incorporated by reference into the Registration Statement and to the reference to this firm under the caption “Legal Matters” in the prospectus which forms a part of the Registration Statement. In giving these consents, we do not hereby admit that we are in the category of persons whose consent is required under Section 7 of the Securities Act.