Exhibit 5.1

Simpson Thacher & Bartlett LLP

425 LEXINGTON AVENUE

NEW YORK, NY 10017-3954

TELEPHONE: +1-212-455-2000

FACSIMILE: +1-212-455-2502

May 25, 2021

First Eagle Alternative Capital BDC, Inc.

500 Boylston Street, Suite 1200,

Boston, MA 02116

Ladies and Gentlemen:

We have acted as counsel to First Eagle Alternative Capital BDC, Inc., a Delaware corporation (the “Company”), in connection with the Registration Statement on Form N-2 (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 from time to time of up to $250,000,000 aggregate initial offering price of debt securities and other securities.

We have examined the Registration Statement, the Underwriting Agreement dated May 18, 2021 (the “Underwriting Agreement”), among the Company, First Eagle Alternative Credit, LLC, a Delaware limited liability company (the “Advisor”), and Keefe, Bruyette & Woods, Inc., as representative of the several underwriters named therein pursuant to which such underwriters have agreed to purchase $60,000,000 aggregate principal amount of 5.00% Notes due 2026 (the “Notes”) issued by the Company; the Indenture, dated as of November 18, 2014 (the “Base Indenture”), between the Company and U.S. Bank National Association, as trustee (the

“Trustee”), as supplemented by the Fourth Supplemental Indenture, dated as of May 25, 2021 (the “Fourth Supplemental Indenture” and, together with the Base Indenture, the “Indenture”); and a duplicate of the global note representing the Notes. In addition, we have examined, and have relied as to 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 Advisor 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. We also have assumed that the Indenture is the valid and legally binding obligation of the Trustee.

In rendering the opinion set forth below, we have assumed further that the execution, issuance, delivery and performance by the Company and the Advisor of the Underwriting Agreement, the Indenture and the Notes, as applicable, do not constitute a breach or default under any agreement or instrument which is binding upon the Company.

Based upon the foregoing, and subject to the qualifications, assumptions and limitations stated herein, we are of the opinion that, assuming due authentication thereof by the Trustee and upon payment and delivery in accordance with the provisions of the Underwriting Agreement, the Notes will constitute valid and legally binding obligations of the Company enforceable against the Company in accordance with their terms.

Our opinion set forth above is subject to (i) the effects of bankruptcy, insolvency, fraudulent conveyance, reorganization, moratorium and other similar laws relating to or affecting creditors’ rights generally, (ii) general equitable principles (whether considered in a proceeding in equity or at law) and (iii) an implied covenant of good faith and fair dealing. In addition, we express no opinion as to the validity, legally binding effect or enforceability of Section 1.09 and Section 8.02 of the Base Indenture relating to the separability of provisions of the Indenture.

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 5 to the Registration Statement and to the use of our name under the caption “Legal Matters” in the prospectus included in the Registration Statement.