Exhibit 32.1

Certification of Chief Executive Officer

Pursuant to

Section 906 of the Sarbanes-Oxley Act of 2002 (18 U.S.C. 1350)

In connection with the annual report on Form 10-K for the year ended September 30, 2014 (the “Report”) of Fifth Street Finance Corp . (the “Registrant”), as filed with the Securities and Exchange Commission on the date hereof, I, Leonard M. Tannenbaum , the Chief Executive Officer of the Registrant, hereby certify, to the best of my knowledge, that:

(1) The Report fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934, as amended; and

(2) The information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Registrant.

/s/    Leonard M. Tannenbaum

Name:    Leonard M. Tannenbaum

Date: November 28, 2014