Exhibit 13.5

Execution Version

AMENDED AND RESTATED
SUPPORT AND NON-ELECTION AGREEMENT

This AMENDED AND RESTATED SUPPORT AND NON-ELECTION AGREEMENT (this “Agreement”) is entered into as of April 24, 2023 by and among Kayne Anderson Energy Infrastructure Fund, Inc., a Maryland corporation (“KYN”), Kayne Anderson NextGen Energy & Infrastructure, Inc., a Maryland corporation (“KMF”), and the undersigned stockholders of KYN and/or KMF (“Stockholders”). KYN, KMF and each Stockholder are collectively referred to herein as the “Parties” and each individually as a “Party.”

WHEREAS, as of the date hereof, each Stockholder is the “beneficial owner” (within the meaning of Rule 13d-3 under the Securities Exchange Act of 1934, as amended (the “Exchange Act”)) of shares of common stock, par value $0.001 per share, of KYN (“KYN Common Stock”), and shares of common stock, par value $0.001 per share, of KMF (“KMF Common Stock”) (together with any other shares of capital stock of KYN or KMF acquired by such Stockholder after the date hereof and prior to the Termination Date (as defined below), and the termination of all of such Stockholder’s obligations under this Agreement, being collectively referred to herein as the “KYN Securities” and “KMF Securities,” respectively; provided, that for the avoidance of doubt, neither KYN Securities nor KMF Securities shall include securities disposed of by such Stockholder in a manner that does not otherwise violate this Agreement);

WHEREAS, KYN and KMF have entered into that certain Amended and Restated Agreement and Plan of Merger, dated as of April 24, 2023 (the “Merger Agreement”), pursuant to which, among other things, KMF would be merged with and into a wholly owned subsidiary of KYN (the “Merger”);

WHEREAS, it is a condition precedent to the consummation of the Merger under the Merger Agreement that (a) the Merger be approved by the stockholders of KMF (the “Merger Approval”) and (b) the issuance of additional shares of KYN Common Stock in connection with the Merger be approved by the stockholders of KYN (the “NYSE Approval”);

WHEREAS, this Agreement amends, restates and replaces the Support and Non-Tender Agreement, dated as of March 24, 2023, among the Parties in order to remove references and obligations with respect to a tender offer by KMF and to reflect the modified merger terms to include an optional election for partial cash consideration; and

WHEREAS, in order to support the Merger Approval and the NYSE Approval, each Stockholder has agreed to enter into this Agreement.

NOW, THEREFORE, in consideration of the premises, covenants and agreements set forth herein, and other good and valuable consideration, the receipt and sufficiency of which are hereby acknowledged, the Parties hereto hereby agree as follows:

1.Agreement to Vote. From and after the date hereof until the Termination Date (as defined below), each Stockholder (in such capacity and not in any other capacity) hereby agrees that, at any meeting (whether annual or special and each adjourned or postponed meeting) of KYN’s or KMF’s stockholders, however called, or in connection with any other written consent of KYN’s or KMF’s stockholders, such Stockholder will (x) appear at such meeting or otherwise cause all of the KYN Securities and KMF Securities, as applicable, to be counted as present thereat for purposes of calculating a quorum and (y) vote or cause to be voted (including by proxy or written consent, if applicable):

(a)all of the KMF Securities in favor of the Merger Approval;

(b)all of the KYN Securities in favor of the NYSE Approval;

(c)all of the KYN Securities and KMF Securities for any proposal to adjourn or postpone the applicable stockholder meeting to a later date proposed by KYN or KMF for purposes of obtaining the Merger Approval or the NYSE Approval;

(d)all of the KYN Securities and KMF Securities against any other action, agreement or transaction, that is intended, that could reasonably be expected, or the effect of which could reasonably be expected, to materially impede, frustrate, prevent, interfere with, delay, postpone, discourage or adversely affect the Merger or any of the other transactions contemplated by the Merger Agreement or this Agreement or the performance by such Stockholder of its obligations under this Agreement; and

(e)all of the KYN Securities and KMF Securities against any action, proposal, transaction or agreement that would reasonably be expected to result in a breach in any respect of any covenant, representation or warranty or any other obligation or agreement of such Stockholder contained in this Agreement.

2.Agreement Not to Elect Cash Consideration. Each Stockholder hereby covenants and agrees not to elect to receive any cash consideration for its KMF Common Stock in connection with the Merger.

3.Representations and Warranties. Each Stockholder (severally and not jointly) represents and warrants to KYN and KMF as follows:

(a)This Agreement has been duly executed and delivered by such Stockholder and, assuming due authorization, execution and delivery by the other Parties, this Agreement constitutes a legally valid and binding obligation of such Stockholder, enforceable against such Stockholder in accordance with the terms hereof (except as enforceability may be limited by bankruptcy laws, other similar laws affecting creditors’ rights and general principles of equity affecting the availability of specific performance and other equitable remedies).

(b)Such Stockholder is the beneficial owner (within the meaning of Rule 13d-3 under the Exchange Act) of, and has good title to, all of the KYN Securities and KMF Securities, and there exist no liens or any other limitation or restriction (including any restriction on the right to vote, sell or otherwise dispose of such securities (other than transfer restrictions under the Securities Act of 1933, as amended)) affecting any such KYN Securities and KMF Securities, other than pursuant to ordinary course brokerage arrangements.

(c)The execution and delivery of this Agreement by such Stockholder does not, and the performance by such Stockholder of its obligations hereunder will not, require any consent or approval that has not been given or other action that has not been taken by any third party (including under any contract binding upon such Stockholder or the KYN Securities and KMF Securities), in each case, to the extent such consent, approval or other action would prevent, enjoin or materially delay the performance by such Stockholder of its obligations under this Agreement.

(d)There are no actions pending against such Stockholder or, to such Stockholder’s knowledge, threatened against such Stockholder, before (or, in the case of threatened actions, that would be before) any arbitrator or any governmental authority, which in any manner challenges or seeks to prevent, enjoin or materially delay the performance by such Stockholder of its obligations under this Agreement.

4.Further Assurances. From time to time, at KYN’s or KMF’s reasonable request and without further consideration, each Stockholder shall execute and deliver such additional documents and take all such further action as may be reasonably necessary or reasonably requested to effect the actions and consummate the transactions contemplated by this Agreement.

5.Assignment. No Party shall assign this Agreement or any part hereof without the prior written consent of the other Parties. Subject to the foregoing, this Agreement shall be binding upon and inure to the benefit of the Parties and their respective permitted successors and assigns. Any attempted assignment in violation of the terms of this Section 5 shall be null and void, ab initio.

2

6.Enforcement. The Parties agree that irreparable damage for which monetary damages, even if available, may not be an adequate remedy, would occur in the event that the Parties do not perform their obligations under the provisions of this Agreement in accordance with their respective specified terms or otherwise breach any of such provisions. Each of the Parties acknowledge and agree that (a) each of the Parties shall be entitled to seek an injunction, specific performance, or other equitable relief, to prevent breaches of this Agreement and to enforce specifically the terms and provisions hereof and thereof, including each Stockholder’s obligations to vote its KYN Securities and KMF Securities as provided in this Agreement, without proof of damages, prior to the valid termination of this Agreement, this being in addition to any other remedy to which they are entitled under this Agreement, and (b) the right of specific enforcement is an integral part of the transactions contemplated by this Agreement and without that right, none of the Parties would have entered into this Agreement. Each Party agrees that it will not oppose the granting of specific performance and other equitable relief on the basis that the other Party have an adequate remedy at applicable law or that an award of specific performance is not an appropriate remedy for any reason at applicable law or equity. The Parties acknowledge and agree that any Party seeking an injunction to prevent breaches of this Agreement and to enforce specifically the terms and provisions of this Agreement in accordance with this Section 6 shall not be required to provide any bond or other security in connection with any such injunction.

7.Governing Law. This Agreement shall be construed and enforced in accordance with, and all questions concerning the construction, validity, interpretation, inducement to enter and/or performance of this Agreement (whether related to breach of contract, tortious conduct or otherwise and whether now existing or hereafter arising) shall be governed by, and construed in accordance with, the laws of the State of Maryland, without regard to the principles of conflicts of laws that would otherwise require the application of the law of any other jurisdiction.

[SIGNATURE PAGE FOLLOWS]

3

Execution Version

IN WITNESS WHEREOF, the Parties hereto have caused this Agreement to be executed as of the date first above written.

KAYNE ANDERSON ENERGY INFRASTRUCTURE FUND, INC.
By:	/s/ James C. Baker, Jr.
	Name:	James C. Baker, Jr.
	Title:	Chairman of the Board of Directors, President and Chief Executive Officer
KAYNE ANDERSON NEXTGEN ENERGY & INFRASTRUCTURE, INC.
By:	/s/ James C. Baker, Jr.
	Name:	James C. Baker, Jr.
	Title:	Chairman of the Board of Directors, President and Chief Executive Officer
JAMES C. BAKER, JR.
	/s/ James C. Baker, Jr.
J.C. FREY
	/s/ J.C. Frey
TERRY A. HART
	/s/ Terry A. Hart
A. COLBY PARKER
	/s/ A. Colby Parker
MICHAEL J. O’NEIL
	/s/ Michael J. O’Neil

4

RON M. LOGAN, JR.
	/s/ Ron M. Logan, Jr.
ADRIANA J. JIMENEZ
	/s/ Adriana J. Jimenez
WILLIAM R. CORDES
	/s/ William R. Cordes
ANNE K. COSTIN
	/s/ Anne K. Costin
BARRY R. PEARL
	/s/ Barry R. Pearl
ALBERT J. RICHEY
	/s/ Albert J. Richey
WILLIAM H. SHEA, JR.
	/s/ William H. Shea, Jr.
CARITA S. WALKER
	/s/ Carita S. Walker
CAROLINE A. WINN
	/s/ Caroline A. Winn

5