Administrative Services Agreement between the Company and the Sponsor

Exhibit 10.5

LEO HOLDINGS CORP.

21 Grosvenor Place

London, SW1X 7HF

February 15, 2018

Leo Investors Limited Partnership

21 Grosvenor Place

London, SW1X 7HF

Ladies and Gentlemen:

This letter 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 Leo Holdings Corp. (the “Company”) and continuing until the earlier of (i) the consummation by the Company of an initial business combination or (ii) the Company’s liquidation (in each case as described in the Registration Statement) (such earlier date hereinafter referred to as the “Termination Date”), Leo Investors Limited Partnership shall 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 21 Grosvenor Place, London, SW1X 7HF (or any successor location). In exchange therefore, the Company shall pay Leo Investors Limited Partnership a sum not to exceed $10,000 per month, respectively, on the Effective Date and continuing monthly thereafter until the Termination Date. Leo Investors Limited Partnership hereby agrees that it does not have any right, title, interest or claim of any kind in or to any monies that may be set aside in a trust account (the “Trust Account”) that may be established upon the consummation of the IPO (the “Claim”) and hereby waives any Claim it may have in the future as a result of, or arising out of, any negotiations, contracts or agreements with the Company and will not seek recourse against the Trust Account for any reason whatsoever.

AGREED TO AND ACCEPTED BY:

LEO INVESTORS LIMITED PARTNERSHIP

By: Leo Investors General Partner Limited,

its general partner

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