Exhibit 10.5

First Amendment to Custody Agreement

This First Amendment
to that certain Custody Agreement by and between Keating Capital, Inc. (Keating Capital) and Steele Street Bank & Trust (the Custodian) dated November 18, 2008 (the Custody Agreement) is hereby
entered into by Keating Capital and the Custodian as of December 21, 2012.

WHEREAS, pursuant to
Addendum A to Custody Agreement dated November 22, 2011, Keating Capital and the Custodian established certain operational procedures relative to the handling of cash transfers from the custody account maintained under the Custody Agreement;
and

WHEREAS, Keating Capital and the Custodian desire to modify certain terms of the Custody Agreement
so that the custody arrangement qualifies as a bank custody arrangement under Section 17(f) of the 40 Act (as defined in the Custody Agreement) and the rules promulgated thereunder, and no longer be considered a self-custody arrangement under
Section 17(f) of the 40 Act and the rules promulgated thereunder; and

WHEREAS, the Board of
Directors of Keating Capital (the Board) has approved this First Amendment to the Custody Agreement (First Amendment) and has revoked the Boards prior resolution authorizing and permitting certain officers of Keating
Capital to have access to, and withdraw from custody, the Securities, Loan Document Files and Loan Documents held in custody; and

WHEREAS, all capitalized terms contained in this First Amendment not otherwise define herein shall have the meaning ascribed to them in the Custody Agreement; and

WHEREAS, Keating Capital and the Custodian desire to enter into this First Amendment to modify and amend the terms
of the Custody Agreement as set forth herein effective as; and

NOW, THEREFORE, the parties hereto
agree as follows:

1. Section 9 of Article III (Custody of Securities and Related Services) is hereby
deleted in its entirety, and Section 10 of Article III is hereby re-numbered as Section 9.

2.
Section 5 of Article V (Custody of Loan Document Files and Related Services) is hereby amended in its entirety to read as follows:

5. No director, officer, employee or agent of Keating Capital shall have physical access to the Loan Document Files or be authorized or permitted to withdraw any Loan Documents nor shall Custodian
deliver any Loan Documents to any such person.

3. Section 3 of Article VII (Sale and Redemption of
Shares) is hereby amended in its entirety to read as follows:

3. Except as provided hereinafter,
whenever Keating Capital desires Custodian to make payment out of the money held by Custodian hereunder in connection with any redemption of Shares, it shall furnish to Custodian a Certificate or Instructions specifying the total amount to be paid
for such Shares. Custodian shall make payment of such total amount to the transfer agent or to any broker acting as an agent for Keating Capital to facilitate such redemptions (as specified in such Certificate or Instructions) out of the money held
in an Account. Any Shares redeemed by Keating Capital may be held by the transfer agent in book entry form. Any redemption of Shares shall be made in accordance with the provisions of the 40 Act and any rules thereunder.



---

4. Section 5 of Article IX (Concerning Custodian) is hereby amended in
its entirety to read as follows:

5. Keating Capital shall pay to Custodian the fees and charges as may
be specifically agreed upon from time to time. As compensation for the Custodians services hereunder Keating Capital agrees to pay an annual fee according to the attached Fee Schedule (Annual Fee), which may be updated from time to
time by the mutual agreement of the parties. Except as agreed to by Keating in advance, (i) the Annual Fee represents the sole compensation due to Custodian for the services provided the Custodian hereunder, and (ii) Custodian shall be
responsible for the payment of all out-of-pocket expenses which are a normal incident of the services provided hereunder. The Custodian is authorized to collect such Annual Fee by withdrawing the pro-rata portion of the Annual Fee from the custody
account monthly and to reflect the payment on the statement for the custody account.

5. A new
Section 9 shall be added under Article IX (Miscellaneous) to read as follows:

9. If and to the
extent that any provision of this Agreement conflicts with any provision of the 40 Act, specifically Section 17(f) and the rules promulgated thereunder, the applicable provision of the 40 Act shall control; provided, however, that
such conflict shall not affect any of the remaining provisions of this Agreement or render invalid or improper any action taken or omitted prior to such determination.

6. Except as set forth herein, the terms and conditions of the Custody Agreement and Addendum A thereto shall remain in
full force and effect.

[Remainder of this page intentionally left blank.]



2



---

IN WITNESS WHEREOF, Keating Capital and Custodian have caused this
First Amendment to be executed by their respective officers, thereunto duly authorized, as of the day and year first above written.



|                      |  |                                               
|--------------------- |  | ----------------------------------------------
|Keating Capital, Inc.
|                      | 
|By:                   |  | /s/ Frederic M. Schweiger                     
|                      |  | Frederic M. Schweiger, Chief Operating Officer



|                           |  |                   
|-------------------------- |  | ------------------
|Steele Street Bank & Trust
|                           | 
|By:                        |  | /s/ Mary K. Rolsch
|                           | 
|Name (print):              |  | Mary K. Rolsch    
|                           | 
|Title:                     |  | Vice President    



3