Exhibit 3.5

CERTIFICATE OF AMENDMENT TO THE

CERTIFICATE OF DESIGNATION OF

7.125% SERIES A CUMULATIVE TERM PREFERRED STOCK

OF

GLADSTONE INVESTMENT CORPORATION

Pursuant to the provisions of Section 242 of the General Corporation Law of the State of Delaware (the “DGCL”), the undersigned corporation hereby adopts the following Certificate of Amendment to its Certificate of Designations of 7.125% Series A Cumulative Term Preferred Stock (“Series A Term Preferred Stock”):

FIRST: The terms and provisions of this Certificate of Amendment have been duly adopted in accordance with Section 242 of the DGCL.

SECOND: Section 2.1(a) shall be deleted and replaced in its entirety with the following:

“A series of 1,600,000 shares of Preferred Stock is hereby designated as the Series A Term Preferred Stock. Each share of Series A Term Preferred Stock shall have such preferences, voting powers, restrictions, limitations as to dividends and distributions, qualifications and terms and conditions of redemption, in addition to those required by applicable law and those that are expressly set forth in the Certificate of Incorporation, as are set forth in this Certificate of Designation. The Series A Term Preferred Stock shall constitute a separate series of Capital Stock and each share of Series A Term Preferred Stock shall be identical. No fractional shares of Series A Term Preferred Stock shall be issued.”

THIRD: Section 1.1 definition of “Mandatory Redemption Price” shall be deleted and replaced in its entirety with the following:

“Mandatory Redemption Price” shall have the meaning as set forth in Section 2.5(b)(i).”

FOURTH: Section 2.6(c)(i) is hereby amended to delete the cross-reference to “Section 2.8” therein and such reference is hereby replaced with the cross-reference to “Section 2.7.”

The amendment was duly adopted by the board of directors of the corporation on October 7, 2014 in accordance with Section 242 of the DGCL.

[Signature Page Follows]

1

IN WITNESS WHEREOF, this Certificate of Amendment has been executed by a duly authorized officer of the corporation as of this 3rd day of August, 2015.

[Signature Page to Certificate of Amendment of Series A Term Preferred Certificate of Designation]