Exhibit 10.5

GRAF INDUSTRIAL CORP.

118 Vintage Park Blvd., Suite W-222

Houston, Texas 77070

October 15, 2018

Graf Acquisition LLC

118 Vintage Park Blvd., Suite W-222

Houston, Texas 77070

Re: Administrative Support Agreement

Ladies and Gentlemen:

This letter agreement (this “Agreement”) by and between Graf Industrial Corp. (the “Company”) and PSI Capital Inc. (“PSI”), dated as of the date hereof, will confirm our agreement that, commencing on the date the securities of the Company are first listed on the New York Stock Exchange (the “Listing Date”), pursuant to a Registration Statement on Form S-1 and prospectus filed with the U.S. Securities and Exchange Commission (the “Registration Statement”) and continuing until the earlier of the consummation by the Company of an initial business combination or the Company’s liquidation (in each case as described in the Registration Statement) (such earlier date hereinafter referred to as the “Termination Date”):

1.            PSI shall make available, or cause to be made available, to the Company, at 118 Vintage Park Blvd., Suite W-222, Houston, Texas 77070 (or any successor location), certain office space, utilities and secretarial and administrative support as may be reasonably required by the Company. In exchange therefor, the Company shall reimburse PSI up to $5,000 per month on the Listing Date and continuing monthly thereafter until the Termination Date; and

2.            PSI 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 established for the benefit of the public stockholders of the Company and into which substantially all of the proceeds of the Company’s initial public offering will be deposited (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.

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.

No party hereto may assign either this Agreement or any of its rights, interests, or obligations hereunder without the prior written approval 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 constitutes the entire relationship of the parties hereto, and any litigation between the parties (whether grounded in contract, tort, statute, law or equity) 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 law principles.

[Signature Page Follows]

Very truly yours,
GRAF INDUSTRIAL CORP.
By:	/s/ James A. Graf
	Name: James A. Graf
	Title: Chief Executive Officer

AGREED AND ACCEPTED BY:
PSI CAPITAL INC.
By:	/s/ James A. Graf
	Name: James A. Graf
	Title: Chief Executive Officer

[Signature Page to Administrative Support Agreement]