Exhibit 32.2

Certification of Chief Financial 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 quarterly period ended December 31, 2014 (the “Report”) of Fifth Street Finance Corp . (the “Registrant”), as filed with the Securities and Exchange Commission on the date hereof, I, Richard A. Petrocelli , the Chief Financial 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/    Richard A. Petrocelli

Name:    Richard A. Petrocelli

Date: February 6, 2015