Exhibit 5.1

Sixth Street Specialty Lending, Inc.

2100 McKinney Avenue, Suite 1500

Dallas, TX 75201

Ladies and Gentlemen:

We have acted as counsel to Sixth Street Specialty Lending, Inc., a Delaware corporation (the “Company”), in connection with the Company’s offering pursuant to a registration statement on Form N-2 (No. 333-231271), as amended as of January 27, 2021 for purposes of Rule 430C(a) under the Securities Act of 1933, as amended (the “Securities Act”) (as so amended, including the documents incorporated by reference therein, but excluding Exhibit (d)(3), the “Registration Statement”), and the prospectus, dated May 7, 2019 (including the documents incorporated by reference therein, the “Base Prospectus”), as supplemented by the prospectus supplement, dated January 27, 2021 (including the documents incorporated by reference therein, the “Prospectus Supplement” and, together with the Base Prospectus, the “Prospectus”), of $300,000,000 aggregate principal amount of 2.500% Notes due 2026 (the “Securities”). The Securities were issued pursuant to an indenture dated as of January 22, 2018 (the “Base Indenture”) between the Company and Wells Fargo Bank, National Association, as trustee (the “Trustee”), as supplemented with respect to the Securities by the Third Supplemental Indenture thereto dated as of February 3, 2021 (the “Supplemental Indenture” and, together with the Base Indenture, the “Indenture”) between the Company and the Trustee.

In arriving at the opinion expressed below, we have reviewed the following documents:

Sixth Street Specialty Lending, Inc., p. 2

In addition, we have reviewed the originals or copies certified or otherwise identified to our satisfaction of all such corporate records of the Company and such other documents, and we have made such investigations of law, as we have deemed appropriate as a basis for the opinion expressed below.

In rendering the opinion expressed below, we have assumed the authenticity of all documents submitted to us as originals and the conformity to the originals of all documents submitted to us as copies. In addition, we have assumed and have not verified the accuracy as to factual matters of each document we have reviewed.

Based on the foregoing, and subject to the further assumptions and qualifications set forth below, it is our opinion that the Securities are the valid, binding and enforceable obligations of the Company, entitled to the benefits of the Indenture.

Insofar as the foregoing opinion relates to the valid existence and good standing of the Company or any subsidiary of the Company, it is based solely on confirmation from public officials. Insofar as the foregoing opinion relates to the validity, binding effect or enforceability of any agreement or obligation of the Company, (x) we have assumed that the Company and each other party to such agreement or obligation has satisfied those legal requirements that are applicable to it to the extent necessary to make such agreement or obligation enforceable against it (except that no such assumption is made as to the Company regarding matters of the law of the State of New York or the General Corporation Law of the State of Delaware that in our experience normally would be applicable to general business entities with respect to such agreement or obligation), (y) we express no opinion with respect to the effect of any mandatory choice of law rules and (z) such opinion is subject to applicable bankruptcy, insolvency and similar laws affecting creditors’ rights generally and to general principles of equity.

The foregoing opinion is limited to the law of the State of New York and the General Corporation Law of the State of Delaware.

Sixth Street Specialty Lending, Inc., p. 3

We hereby consent to the use of our name in the Prospectus Supplement and the Prospectus under the headings “Legal Matters” as counsel for the Company that has passed on the validity of the Securities, and to the use of this opinion as Exhibit 5.1 to the Company’s Current Report on Form 8-K dated February 3, 2021. In giving this consent, we do not thereby admit that we are within 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 thereunder.

The opinion expressed herein is rendered on and as of the date hereof, and we assume no obligation to advise you or any other person, or to make any investigations, as to any legal developments or factual matters arising subsequent to the date hereof that might affect the opinion expressed herein.