Exhibit 99.5

Lock-up Agreement

November 21, 2019

Raymond James & Associates, Inc.

880 Carillon Parkway

St. Petersburg, Florida 33716

As Representative of the Several Underwriters

Re: Alpine Income Property Trust, Inc. (the “Company”) - Restriction on Stock Sales

Dear Sirs:

This letter is delivered to you pursuant to the Underwriting Agreement (the “Underwriting Agreement”) to be entered into by the Company, as issuer, Alpine Income Property OP, LP (the “Operating Partnership”), Alpine Income Property Manager, LLC (the “Manager”) and Raymond James & Associates, Inc. as the representative (the “Representative”) of certain underwriters (the “Underwriters”) to be named therein. Upon the terms and subject to the conditions of the Underwriting Agreement, the Underwriters intend to effect a public offering (the “Offering”) of the Company’s common stock, par value $0.01 per share (the “Shares”), as described in and contemplated by the registration statement of the Company on Form S-11 (File No. 333-234304) (the “Registration Statement”).

The undersigned recognizes that it is in the best financial interests of the undersigned, as an officer or director, or an owner of stock, options, warrants or other securities of the Company (the “Company Securities”), that the Company complete the proposed Offering.

The undersigned further recognizes that the Company Securities held by the undersigned are, or may be, subject to certain restrictions on transferability, including those imposed by United States federal securities laws. Notwithstanding these restrictions, the undersigned has agreed to enter into this letter agreement to further assure the Underwriters that the Company Securities of the undersigned, now held or hereafter acquired, will not enter the public market at a time that might impair the underwriting effort.

Therefore, as an inducement to the Underwriters to execute the Underwriting Agreement, the undersigned hereby acknowledges and agrees that the undersigned will not, directly or indirectly, (i) offer, pledge, sell, contract to sell, contract to purchase, grant any option, right or warrant to purchase, lend or otherwise dispose of (or enter into any transaction or device that is designed to, or could be expected to, result in the disposition by any person at any time in the future of) any Company Securities (collectively, a “Disposition”), or any securities convertible into or exercisable or exchangeable for, or any rights to purchase or otherwise acquire, any Company Securities held by the undersigned or acquired by the undersigned after the date hereof, or that may be deemed to be beneficially owned by the undersigned (collectively, the “Lock-Up Securities”), pursuant to the Rules and Regulations promulgated under the Securities Act of

1933, as amended (the “Act”), and the Securities Exchange Act of 1934, as amended (the “Exchange Act”), for a period commencing on the date hereof and ending 180 days after the date of the Company’s prospectus first filed pursuant to Rule 424(b) under the Act, inclusive (the “Lock-Up Period”), without the prior written consent of Raymond James & Associates, Inc., (ii) enter into any swap or other agreement that transfers to another, in whole or in part, any of the economic consequences of ownership of such Lock-Up Securities, whether any such transaction described in clause (i) or (ii) above is to be settled by delivery of the Lock-Up Securities or other Company Securities, in cash or otherwise, or (iii) exercise or seek to exercise or effectuate in any manner any rights of any nature that the undersigned has or may have hereafter to require the Company to register under the Act the undersigned’s sale, transfer or other disposition of any of the Lock-Up Securities or other securities of the Company held by the undersigned, or to otherwise participate as a selling securityholder in any manner in any registration effected by the Company under the Act, including under the Registration Statement, during the Lock-Up Period. The foregoing restrictions are expressly agreed to preclude the undersigned from engaging in any hedging, collar (whether or not for any consideration) or other transaction that is designed to or reasonably expected to lead or result in a Disposition of Lock-Up Securities during the Lock-Up Period, even if such Lock-Up Securities would be disposed of by someone other than such holder. Such prohibited hedging or other transactions would include any short sale or any purchase, sale or grant of any right (including any put or call option or reversal or cancellation thereof) with respect to any Lock-Up Securities or with respect to any security (other than a broad-based market basket or index) that includes, relates to or derives any significant part of its value from Lock-Up Securities.

If the undersigned is an officer or director of the Company, (i) the Representative agrees that, at least three business days before the effective date of any release or waiver of the foregoing restrictions in connection with a transfer of shares of the Company’s common stock, par value $0.01 per share (“Common Stock”), the Representative will notify the Company of the impending release or waiver and (ii) the Company will agree in the Underwriting Agreement to announce the impending release or waiver by press release through a major news service at least two business days before the effective date of the release or waiver. Any release or waiver granted by the Representative hereunder to any such officer or director shall only be effective two business days after the publication date of such press release. The provisions of this paragraph will not apply if (i) the release or waiver is effected solely to permit a transfer not for consideration and (ii) the transferee has agreed in writing to be bound by the same terms described in this letter to the extent and for the duration that such terms remain in effect at the time of the transfer.

Notwithstanding the agreement not to make any Disposition during the Lock-Up Period, the Representative has agreed that the undersigned may transfer the undersigned’s Lock-Up Securities (i) as a bona fide gift or gifts; (ii) to any trust for the direct or indirect benefit of the undersigned or the immediate family of the undersigned or if the undersigned is a trust, to any trust beneficiary (including such trust beneficiary’s estate) of the undersigned; (iii) by will or intestate succession upon the death of the undersigned; (iv) as a distribution to members, limited partners or stockholders of the undersigned; (v) to the undersigned’s affiliates; or (vi) with the prior written consent of the Representative on behalf of the Underwriters; provided, however, that in the case of any transfer pursuant to (i), (ii),(iii), (iv) or (v) above, it shall be a condition to the transfer that the donee, trustee, heir, or other transferee, as the case may be, agree to be bound

in writing by the restrictions set forth herein; provided, further, that any transfer pursuant to (i), (ii), (iii), (iv) or (v) above shall not involve a disposition for value; provided, further, that no filing by the undersigned or any other party (including any donor, donee, transferor or transferee) under the Exchange Act or other public announcement reporting a reduction in beneficial ownership of shares of Common Stock held by the undersigned shall be required or shall be made voluntarily in connection with such transfer. For purposes of this letter, “immediate family” shall mean any relationship by blood, marriage or adoption, not more remote than first cousin.

It is understood that, if the Underwriting Agreement (other than the provisions thereof that survive termination) shall terminate or be terminated prior to payment for and delivery of the Shares, the Representative will release the undersigned from the obligations under this letter agreement.

In furtherance of the foregoing, the Company and its transfer agent and registrar are hereby authorized to decline to make any transfer of Lock-Up Securities if such transfer would constitute a violation or breach of this letter. This letter shall be binding on the undersigned and the respective successors, heirs, personal representatives and assigns of the undersigned. Capitalized terms used but not defined herein have the respective meanings assigned to such terms in the Underwriting Agreement.

Very truly yours,

/s/ Steven R. Greathouse

Steven R. Greathouse

[Signature Page to Lock-Up Agreement]