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 Quarterly Report on Form 10-Q for the quarter ended June 30, 2012 (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.