Sixth Street Specialty Lending (TSLX) 8-K Other Events

Exhibit 5.1

Simpson Thacher & BartlettLLP

900GSTREET,NW

WASHINGTON,D.C. 20001

TELEPHONE: +1-202-636-5500

FACSIMILE: +1-202-636-5502

Direct Dial Number +1-202-636-5543 E-mail Address rajib.chanda@stblaw.com

March 5, 2024

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 Registration Statement on Form N-2 (File No. 333-276252) (the “Registration Statement”) filed by the Company with the Securities and Exchange Commission (the “Commission”) under the Securities Act of 1933, as amended, relating to the issuance by the Company of up to 4,000,000 shares of Common Stock, par value $0.01 per share (“Common Stock”) of the Company.

We have examined the Registration Statement, the Underwriting Agreement dated February 29, 2024 (the “Underwriting Agreement”), among the Company, Sixth Street Specialty Lending Advisers, LLC, a Delaware limited liability company (the “Adviser”) and Morgan Stanley & Co. LLC as representative of the several underwriters named therein pursuant to which such underwriters have agreed to purchase up to 4,000,000 shares of Common Stock issued by the Company (the “Shares”). In addition, we have examined, and have relied as to

Sixth Street Specialty Lending, Inc. 2 March 5, 2024

matters of fact upon, originals, or duplicates or certified or conformed copies, of such records, agreements, documents and other instruments and such certificates or comparable documents of public officials and of officers and representatives of the Company and the Adviser and have made such other investigations as we have deemed relevant and necessary in connection with the opinion hereinafter set forth.

In rendering the opinion set forth below, we have assumed the genuineness of all signatures, the legal capacity of natural persons, the authenticity of all documents submitted to us as originals, the conformity to original documents of all documents submitted to us as duplicates or certified or conformed copies and the authenticity of the originals of such latter documents.

Based upon the foregoing, and subject to the qualifications, assumptions and limitations stated herein, we are of the opinion that, upon payment and delivery in accordance with the provisions of the Underwriting Agreement, the Shares will be validly issued, fully paid and nonassessable.

We do not express any opinion herein concerning any law other than the law of the State of New York and the Delaware General Corporation Law.

We hereby consent to the filing of this opinion letter as Exhibit (l) to the Registration Statement and to the use of our name under the caption “Legal Matters” in the prospectus included in the Registration Statement.

Very truly yours,

/s/ Simpson Thacher & Bartlett LLP

SIMPSON THACHER & BARTLETT LLP