Exhibit 10.5

INVESTINDUSTRIAL ACQUISITION CORP.

Suite 1, 3rd Floor, 11-12 St James’ Square

London SW1Y 4LB

United Kingdom

November 23, 2020

Investindustrial Acquisition Corp. L.P.

Suite 1, 3rd Floor, 11-12 St James’ Square

London SW1Y 4LB

United Kingdom

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
Investindustrial Acquisition Corp. (the “Company”) and continuing until the
earlier of (i) the consummation by the Company of an initial 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”), Investindustrial Acquisition Corp. L.P. (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 Suite 1, 3rd Floor, 11-12 St James’
Square, London SW1Y 4LB, United Kingdom (or any successor location). In exchange
therefore, the Company shall pay the Sponsor a sum of up to $10,000 per month on
the Effective Date and continuing monthly thereafter until the Termination Date.
The Sponsor hereby agrees that it does not have any right, title, interest or
claim of any kind (a “Claim”) 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 and hereby irrevocably 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.

This letter 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 letter 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 letter agreement and any of their rights,
interests, or obligations hereunder without the consent of the other party.

This letter 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 letter 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 letter agreement.

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Very truly yours, INVESTINDUSTRIAL ACQUISITION CORP. By:  

/s/ Roberto Ardagna

Name:   Roberto Ardagna Title:   Chief Executive Officer

AGREED TO AND ACCEPTED BY:

INVESTINDUSTRIAL ACQUISITION CORP. L.P.

ACTING BY ITS GENERAL PARTNER,

ACQUISITION CORP. GP LIMITED

 

By:  

/s/ Gayle Swanson

Name:   Gayle Swanson Title:   Director By:  

 

Name:   Title: