Exhibit 10.5

PERIMETER ACQUISITION CORP. I

6060 N. Central Express Way Suite 500

Dallas, Texas 75204

[●], 2025

Perimeter Acquisition Sponsor LLC

6060 N. Central Express Way Suite 500

Dallas, Texas 75204

Ladies and Gentlemen:

This letter agreement (this “Agreement”) will confirm our agreement that, commencing on the effective date (the “Effective Date”) of the registration statement (the “Registration Statement”) for the initial public offering (the “IPO”) of the securities of Perimeter Acquisition Corp. I (the “Company”) and continuing until the earlier of (i) the consummation by the Company of an initial business combination (the “Business Combination”) and (ii) the Company’s liquidation (in each case as described in the Registration Statement) (such earlier date hereinafter referred to as the “Termination Date”), Perimeter Acquisition Sponsor LLC (the “Sponsor”) shall take steps directly or indirectly to make available to the Company certain office space, secretarial and administrative services as may be required by the Company from time to time, situated at 6060 N. Central Express Way Suite 500, Dallas, Texas 75204 (or any successor location). In exchange therefor, the Company shall pay the Sponsor or one of its affiliates a sum of $10,000 per month commencing on the Effective Date and continuing monthly thereafter until the Termination Date.

Further, to the fullest extent permitted by applicable law, the Company agrees to defend, indemnify, hold harmless and exonerate (including the advancement of expenses to the fullest extent permitted by applicable law) the Sponsor, its directors, officers, employees, principals, managers, partners, members, shareholders, equityholders, control persons, affiliates, agents, advisors, consultants and representatives (the “Indemnitees”), from any claims, losses, liabilities, obligations, causes of action, proceedings (whether pending or threatened), investigations, damages, awards, settlements, judgments, decrees, fees, costs, penalties, amounts paid in settlement or expenses (including interest, assessments and other charges in connection therewith and reasonable fees and disbursements of attorneys and other professional advisors and costs of suit) (A) arising out of or relating to any pending or threatened claim, action, suit, proceeding or investigation against any of them or in which any of them may be a participant or may otherwise be involved (including as a witness) and/or (B) arising out of or relating to any of the Indemnitees’ activities in connection with the Company’s affairs, including, but not limited to, any such claims, made by the Company or another person, (i) arising out of or relating to the IPO or the Company’s operations or conduct of its business (including, for the avoidance of doubt, the consummation of a Business Combination or the provision of any services between the Company and any Indemnitee), (ii) in respect of any investment opportunities sourced by the Sponsor and its affiliates, and/or (iii) against the Sponsor alleging any expressed or implied management or endorsement by the Sponsor of any of the Company’s activities or any express or implied association between the Sponsor, on the one hand, and the Company or any of its other affiliates, on the other hand. The Indemnitee will promptly notify the Company in writing of any indemnified claim, provided that failure or delay to give such notice shall not relieve the Company of its indemnification obligations hereunder. The Company will, at its expense, undertake the defense of such claim with attorneys of its own choosing reasonably satisfactory in all respects to such Indemnitee, subject to the right of such Indemnitee to undertake such defense as hereinafter provided. An Indemnitee may participate in such defense with counsel of such Indemnitee’s choosing at the expense of the Company. In the event that the Company does not undertake the defense of any claim within a reasonable time after such Indemnitee has given the notice thereof, or in the event that such Indemnitee shall in good faith determine that the defense of any claim by the Company is inadequate or may conflict with the interest of any Indemnitee, such Indemnitee may, at the expense of the Company and after giving notice to the Company of such action, undertake the defense of the claim and compromise or settle the claim, all for the account of and at the risk of the Company. The Company shall pay all costs and expenses (including, without limitation, attorneys’ fees and costs of experts) incurred by the Indemnitee in connection with Indemnitee’s defense of any such claim promptly (and in any event within 10 days) after receipt of any statement therefor. In the defense of any claim against an Indemnitee, the Company shall not, except with the prior written consent of such Indemnitee, consent to entry of any judgment or enter into any settlement that includes any injunctive or other non-monetary relief or any payment of money by such Indemnitee, or that does not include as an unconditional term thereof the giving by the person or persons asserting such claim to such Indemnitee of an unconditional release from all liability on any of the matters that are the subject of such claim and an acknowledgement that such Indemnitee denies all wrongdoing in connection with such matters. The Company shall not be obligated to indemnify an Indemnitee against amounts paid in settlement of a claim if such settlement is effected by such Indemnitee without the prior written consent of the Company, which shall not be unreasonably withheld or delayed. If the indemnification provided for in this paragraph is for any reason not available to an Indemnitee as a matter of law in respect of any losses, claims, damages or liabilities referred to herein, then, in lieu of indemnifying such Indemnitee therefor, the Company shall contribute to the amount paid or payable by such Indemnitee as a result of such losses, claims, damages or liabilities (and expenses relating thereto) (a) in such proportion as is appropriate to reflect the relative benefits to the Indemnitee, on the one hand, and the Company, on the other hand, of the subject matter of this Agreement or (b) if the allocation provided by clause (a) above is not available, in such proportion as is appropriate to reflect not only the relative benefits referred to in such clause (a) but also the relative fault of each of such Indemnitee and the Company, as well as any other relevant equitable considerations. Notwithstanding anything to the contrary set forth herein or otherwise, the Company acknowledges and agrees that each Indemnitee shall be an express third-party beneficiary of the provisions of this paragraph and any related provision hereof that is or may extend rights to such Indemnitee. For the avoidance of doubt, the Company’s indemnification obligations contained in this paragraph shall survive the Company’s consummation of a Business Combination.

The Sponsor hereby irrevocably waives any and all right, title, interest, causes of action and claims of any kind as a result of, or arising out of, this Agreement (each, a “Claim”) in or to, and any and all right to seek payment of any amounts due to it out of, the trust account that was established by the Company in connection with the consummation of the IPO (the “Trust Account”), and hereby irrevocably waives any Claim it may have in the future as a result of, or arising out of, this Agreement, which Claim would reduce, encumber or otherwise adversely affect the Trust Account or any monies or other assets in the Trust Account, and further agrees not to seek recourse, reimbursement, payment or satisfaction of any Claim against the Trust Account or any monies or other assets in the Trust Account for any reason whatsoever. Accordingly, the Sponsor acknowledges and agrees that any indemnification or advance of expenses required to be provided hereunder will only be paid by the Company (i) if prior to a Business Combination, to the extent that the Company has sufficient funds outside of the Trust Account to satisfy its obligations to provide such indemnification and advancement of expenses, or (ii) on or after the date that the Company consummates a Business Combination, and in both cases such indemnification and other payments shall accrue and become due and payable immediately upon the occurrence of either event in clauses (i) and (ii). The Sponsor hereby agrees that any amounts for indemnification or the advancement of expenses required to be provided to the Indemnitees under this Agreement shall be offset against any amounts required to be paid by the Sponsor to the Company pursuant to the Sponsor’s indemnification obligations included in Section 8 of the letter agreement, dated the day hereof, by and among the Company and the Sponsor.

This Agreement constitutes the entire agreement and understanding of the parties hereto in respect of its subject matter and supersedes all prior understandings, agreements, or representations by or among the parties hereto, written or oral, to the extent they relate in any way to the subject matter hereof or the transactions contemplated hereby.

This Agreement may not be amended, modified or waived as to any particular provision, except by a written instrument executed by the parties hereto.

The parties may not assign this Agreement and any of their rights, interests, or obligations hereunder without the consent of the other party. Any purported assignment in violation of this paragraph shall be void and ineffectual and shall not operate to transfer or assign any interest or title to the purported assignee.

This Agreement shall be governed by, construed in accordance with, and interpreted pursuant to the laws of the State of New York, without giving effect to its choice of laws principles that will apply the laws of another jurisdiction.

This Agreement may be executed in one or more counterparts, each of which shall for all purposes be deemed to be an original but all of which together shall constitute one and the same agreement. Only one such counterpart signed by the party against whom enforceability is sought needs to be produced to evidence the existence of this Agreement.

[Signature Page Follows]

Very truly yours,

PERIMETER ACQUISITION CORP. I

By:
Name:	Josef Valdman
Title:	Chief Executive Officer

AGREED TO AND ACCEPTED BY:

PERIMETER ACQUISITION SPONSOR LLC

By:
Name:	Jordan Blashek
Title:	Authorized Signatory

Perimeter Acquisition Corp. I S-1/A