Exhibit 10.5

PRIVATE PLACEMENT WARRANTS PURCHASE AGREEMENT

THIS PRIVATE PLACEMENT WARRANTS PURCHASE AGREEMENT, effective as of April 12,
2018 (as it may from time to time be amended, this “Agreement”), is entered into
by and among Pure Acquisition Corp., a Delaware corporation (the “Company”), and
HighPeak Pure Acquisition, LLC, a Delaware limited liability company (the
“Purchaser”).

WHEREAS

The Company intends to consummate an initial public offering of the Company’s
units (the “Public Offering”), each unit consisting of one share of the
Company’s Class A common stock, par value $0.0001 per share (each, a “Share”),
and one-half of one warrant as set forth in the Company’s registration statement
on Form S-1, filed with the Securities and Exchange Commission (the “SEC”) (the
“Registration Statement”), under the Securities Act of 1933, as amended (the
“Securities Act”);

Each whole warrant entitles the holder to purchase one Share at an exercise
price of $11.50 per Share; and

The Purchaser has agreed to purchase an aggregate of 9,200,000 warrants (or up
to 10,280,000 warrants if the over-allotment option in connection with the
Public Offering is exercised in full) (the “Private Placement Warrants”), each
Private Placement Warrant entitling the holder to purchase one Share at an
exercise price of $11.50 per Share.

NOW THEREFORE, in consideration of the mutual promises contained in this
Agreement and other good and valuable consideration, the receipt and sufficiency
of which are hereby acknowledged, the parties to this Agreement hereby,
intending legally to be bound, agree as follows:

AGREEMENT

Section 1. Authorization, Purchase and Sale; Terms of the Private Placement
Warrants.

 

  A. Authorization of the Private Placement Warrants. The Company has duly
authorized the issuance and sale of the Private Placement Warrants to the
Purchaser.

 

  B. Purchase and Sale of the Private Placement Warrants. On the date one
business day prior to the date of the consummation of the Public Offering or on
such earlier time and date as may be mutually agreed by the Purchaser and the
Company (the “Initial Closing Date”), the Company shall issue and sell to the
Purchaser, and the Purchaser shall purchase from the Company 9,200,000 Private
Placement Warrants at a price of $1.00 per warrant for an aggregate purchase
price of $9,200,000 (the “Purchase Price”), which shall be paid by wire transfer
of immediately available funds to the Company in accordance with the Company’s
wiring instructions. On the Initial Closing Date, upon the payment by the
Purchaser of the Purchase Price payable by it by wire transfer of immediately
available funds to the Company, the Company, at its option, shall effect
delivery in book-entry form of the Private Placement Warrants purchased by the
Purchaser on such date duly registered in the Purchaser’s name to the Purchaser.
On the date one business day prior to each date of the consummation of the
closing of the over-allotment option in connection with the Public Offering or
on such earlier time and date as may be mutually agreed by the Purchaser and the
Company (each such date, an “Over-allotment Closing Date,” and each
Over-allotment Closing Date (if any) and the Initial Closing Date being
sometimes referred to herein as a “Closing Date”), the Company shall issue and
sell to the Purchaser, and the Purchaser shall purchase from the Company, up to
an aggregate of 1,080,000 Private Placement Warrants at a price of $1.00 per
warrant for an aggregate purchase price of up to $1,080,000 (if the
over-allotment option in connection with the Public Offering is exercised in
full) (the “Over-allotment Purchase Price”), which shall be paid by wire
transfer of immediately available funds to the Company in accordance with the
Company’s wiring instructions. On the Over-allotment Closing Date, upon the
payment by the Purchaser of the Over-allotment Purchase Price payable by it by
wire transfer of immediately available funds to the Company, the Company shall,
at its option, deliver a certificate evidencing the Private Placement Warrants
purchased by the Purchaser on such date duly registered in the Purchaser’s name
to the Purchaser, or effect such delivery in book-entry form.

 

  C. Terms of the Private Placement Warrants.

 

  (i) Each Private Placement Warrant shall have the terms set forth in a Warrant
Agreement to be entered into by the Company and a warrant agent, in connection
with the Public Offering (the “Warrant Agreement”).

 

  (ii) At the time of the closing of the Public Offering, the Company and the
Purchaser shall enter into a registration rights agreement (the “Registration
Rights Agreement”) pursuant to which the Company will grant certain registration
rights to the Purchaser relating to the Private Placement Warrants and the
Shares underlying the Private Placement Warrants.

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Section 2. Representations and Warranties of the Company. As a material
inducement to the Purchaser to enter into this

Agreement and purchase the Private Placement Warrants, the Company hereby
represents and warrants to the Purchaser (which representations and warranties
shall survive each Closing Date) that:

 

  A. Organization and Corporate Power. The Company is a corporation duly
organized, validly existing and in good standing under the laws of the State of
Delaware and is qualified to do business in every jurisdiction in which the
failure to so qualify would reasonably be expected to have a material adverse
effect on the financial condition, operating results or assets of the Company.
The Company possesses all requisite corporate power and authority necessary to
carry out the transactions contemplated by this Agreement and the Warrant
Agreement.

 

  B. Authorization; No Breach.

 

  (i) The execution, delivery and performance of this Agreement and the Private
Placement Warrants have been duly authorized by the Company as of the Closing
Date. This Agreement constitutes the valid and binding obligation of the
Company, enforceable in accordance with its terms. Upon issuance in accordance
with, and payment pursuant to, the terms of the Warrant Agreement and this
Agreement, the Private Placement Warrants will constitute valid and binding
obligations of the Company, enforceable in accordance with their terms as of the
Closing Date.

 

  (ii) The execution and delivery by the Company of this Agreement and the
Private Placement Warrants, the issuance and sale of the Private Placement
Warrants, the issuance of the Shares upon exercise of the Private Placement
Warrants and the fulfillment of and compliance with the respective terms hereof
and thereof by the Company, do not and will not as of the Closing Date
(a) conflict with or result in a breach of the terms, conditions or provisions
of, (b) constitute a default under, (c) result in the creation of any lien,
security interest, charge or encumbrance upon the Company’s capital stock or
assets under, (d) result in a violation of, or (e) require any authorization,
consent, approval, exemption or other action by or notice or declaration to, or
filing with, any court or administrative or governmental body or agency pursuant
to the Certificate of Incorporation of the Company or the Bylaws of the Company
(in effect on the date hereof or as may be amended prior to completion of the
contemplated Public Offering), or any material law, statute, rule or regulation
to which the Company is subject, or any agreement, order, judgment or decree to
which the Company is subject, except for any filings required after the date
hereof under federal or state securities laws.

 

  C. Title to Securities. Upon issuance in accordance with, and payment pursuant
to, the terms hereof and the Warrant Agreement, the Shares issuable upon
exercise of the Private Placement Warrants will be duly and validly issued,
fully paid and nonassessable. Upon issuance in accordance with, and payment
pursuant to, the terms hereof and the Warrant Agreement, the Purchaser will have
good title to the Private Placement Warrants purchased by it and the Shares
issuable upon exercise of such Private Placement Warrants, free and clear of all
liens, claims and encumbrances of any kind, other than (i) transfer restrictions
hereunder and under the other agreements contemplated hereby, (ii) transfer
restrictions under federal and state securities laws, and (iii) liens, claims or
encumbrances imposed due to the actions of the Purchaser.

 

  D. Governmental Consents. No permit, consent, approval or authorization of, or
declaration to or filing with, any governmental authority is required in
connection with the execution, delivery and performance by the Company of this
Agreement or the consummation by the Company of any other transactions
contemplated hereby.

Section 3. Representations and Warranties of the Purchaser. As a material
inducement to the Company to enter into this

Agreement and issue and sell the Private Placement Warrants to the Purchaser,
the Purchaser hereby represents and warrants to the Company (which
representations and warranties shall survive each Closing Date) that:

 

  A. Organization and Requisite Authority. The Purchaser possesses all requisite
power and authority necessary to carry out the transactions contemplated by this
Agreement.

 

  B. Authorization; No Breach.

 

  (i) This Agreement constitutes a valid and binding obligation of the
Purchaser, enforceable in accordance with its terms, subject to bankruptcy,
insolvency, fraudulent conveyance, reorganization, moratorium and other laws of
general applicability relating to or affecting creditors’ rights and to general
equitable principles (whether considered in a proceeding in equity or law).

 

  (ii) The execution and delivery by the Purchaser of this Agreement and the
fulfillment of and compliance with the terms hereof by the Purchaser does not
and shall not as of each Closing Date conflict with or result in a breach by the
Purchaser of the terms, conditions or provisions of any agreement, instrument,
order, judgment or decree to which the Purchaser is subject.

 

  C. Investment Representations.

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  (i) The Purchaser is acquiring the Private Placement Warrants and, upon
exercise of the Private Placement Warrants, the Shares issuable upon such
exercise (collectively, the “Securities”) for the Purchaser’s own account, for
investment purposes only and not with a view towards, or for resale in
connection with, any public sale or distribution thereof.

 

  (ii) The Purchaser is an “accredited investor” as such term is defined in Rule
501(a)(3) of Regulation D under the Securities Act.

 

  (iii) The Purchaser understands the Securities are being offered and will be
sold to it in reliance on specific exemptions from the registration requirements
of the United States federal and state securities laws and that the Company is
relying upon the truth and accuracy of, and the Purchaser’s compliance with, the
representations and warranties of the Purchaser set forth herein to determine
the availability of such exemptions and the eligibility of the Purchaser to
acquire such Securities.

 

  (iv) The Purchaser decided to enter into this Agreement not as a result of any
general solicitation or general advertising within the meaning of Rule 502(c)
under the Securities Act.

 

  (v) The Purchaser has been furnished with all materials relating to the
business, finances and operations of the Company and materials relating to the
offer and sale of the Securities which have been requested by the Purchaser. The
Purchaser has been afforded the opportunity to ask questions of the executive
officers and directors of the Company. The Purchaser understands its investment
in the Securities involves a high degree of risk and it has sought such
accounting, legal and tax advice as it has considered necessary to make an
informed investment decision with respect to the acquisition of the Securities.

 

  (vi) The Purchaser understands no United States federal or state agency or any
other government or governmental agency has passed on or made any recommendation
or endorsement of the Securities or the fairness or suitability of the
investment in the Securities by the Purchaser nor have such authorities passed
upon or endorsed the merits of the offering of the Securities.

 

  (vii) The Purchaser understands: (a) the Securities have not been and are not
being registered under the Securities Act or any state securities laws, and may
not be offered for sale, sold, assigned or transferred unless (1) subsequently
registered thereunder or (2) sold in reliance on an exemption therefrom; and
(b) except as specifically set forth in the Registration Rights Agreement,
neither the Company nor any other person is under any obligation to register the
Securities under the Securities Act or any state securities laws or to comply
with the terms and conditions of any exemption thereunder. In this regard, the
Purchaser understands the SEC has taken the position that promoters or
affiliates of a blank check company and their transferees, both before and after
a business combination, are deemed to be “underwriters” under the Securities Act
when reselling the securities of a blank check company. Based on that position,
Rule 144 adopted pursuant to the Securities Act would not be available for
resale transactions of the Securities despite technical compliance with the
requirements of such Rule, and the Securities can be resold only through a
registered offering or in reliance upon another exemption from the registration
requirements of the Securities Act.

 

  (viii) The Purchaser has such knowledge and experience in financial and
business matters, knows of the high degree of risk associated with investments
in the securities of companies in the development stage such as the Company, is
capable of evaluating the merits and risks of an investment in the Securities
and is able to bear the economic risk of an investment in the Securities in the
amount contemplated hereunder for an indefinite period of time. The Purchaser
has adequate means of providing for its current financial needs and
contingencies and will have no current or anticipated future needs for liquidity
which would be jeopardized by the investment in the Securities. The Purchaser
can afford a complete loss of its investment in the Securities.

Section 4. Conditions of the Purchaser’s Obligations. The obligations of the
Purchaser to purchase and pay for the Private

Placement Warrants are subject to the fulfillment, on or before each Closing
Date, of each of the following conditions:

 

  A. Representations and Warranties. The representations and warranties of the
Company contained in Section 2 shall be true and correct at and as of such
Closing Date as though then made.

 

  B. Performance. The Company shall have performed and complied with all
agreements, obligations and conditions contained in this Agreement that are
required to be performed or complied with by it on or before such Closing Date.

 

  C. No Injunction. No litigation, statute, rule, regulation, executive order,
decree, ruling or injunction shall have been enacted, entered, promulgated or
endorsed by or in any court or governmental authority of competent jurisdiction
or any self-regulatory organization having authority over the matters
contemplated hereby, which prohibits the consummation of any of the transactions
contemplated by this Agreement or the Warrant Agreement.

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  D. Warrant Agreement. The Company shall have entered into a Warrant Agreement
with a warrant agent on terms satisfactory to the Purchaser.

Section 5. Conditions of the Company’s Obligations. The obligations of the
Company to the Purchaser under this Agreement are subject to the fulfillment, on
or before each Closing Date, of each of the following conditions:

 

  A. Representations and Warranties. The representations and warranties of the
Purchaser contained in Section 3 shall be true and correct at and as of such
Closing Date as though then made.

 

  B. Performance. The Purchaser shall have performed and complied with all
agreements, obligations and conditions contained in this Agreement that are
required to be performed or complied with by the Purchaser on or before such
Closing Date.

 

  C. Corporate Consents. The Company shall have obtained the consent of its
Board of Directors authorizing the execution, delivery and performance of this
Agreement and the Warrant Agreement and the issuance and sale of the Private
Placement Warrants hereunder.

 

  D. No Injunction. No litigation, statute, rule, regulation, executive order,
decree, ruling or injunction shall have been enacted, entered, promulgated or
endorsed by or in any court or governmental authority of competent jurisdiction
or any self-regulatory organization having authority over the matters
contemplated hereby, which prohibits the consummation of any of the transactions
contemplated by this Agreement or the Warrant Agreement.

 

  E. Warrant Agreement. The Company shall have entered into a Warrant Agreement
with a warrant agent on terms satisfactory to the Company.

Section 6. Termination. This Agreement may be terminated at any time after
July 31, 2018 upon the election by either the Company or the Purchaser upon
written notice to the other party if the closing of the Public Offering does not
occur prior to such date.

Section 7. Survival of Representations and Warranties. All of the
representations and warranties contained herein shall survive each Closing Date.

Section 8. Definitions. Terms used but not otherwise defined in this Agreement
shall have the meaning assigned to such terms in the Registration Statement.

Section 9. Miscellaneous.

 

  A. Successors and Assigns. Except as otherwise expressly provided herein, all
covenants and agreements contained in this Agreement by or on behalf of any of
the parties hereto shall bind and inure to the benefit of the respective
successors of the parties hereto whether so expressed or not. Notwithstanding
the foregoing or anything to the contrary herein, the parties may not assign
this Agreement, other than assignments by the Purchaser to affiliates thereof
(including, without limitation one or more of its members).

 

  B. Severability. Whenever possible, each provision of this Agreement shall be
interpreted in such manner as to be effective and valid under applicable law,
but if any provision of this Agreement is held to be prohibited by or invalid
under applicable law, such provision shall be ineffective only to the extent of
such prohibition or invalidity, without invalidating the remainder of this
Agreement.

 

  C. Counterparts. This Agreement may be executed simultaneously in two or more
counterparts, none of which need contain the signatures of more than one party,
but all such counterparts taken together shall constitute one and the same
agreement.

 

  D. Descriptive Headings; Interpretation. The descriptive headings of this
Agreement are inserted for convenience only and do not constitute a substantive
part of this Agreement. The use of the word “including” in this Agreement shall
be by way of example rather than by limitation.

 

  E. Governing Law. This Agreement shall be deemed to be a contract made under
the laws of the State of New York and for all purposes shall be construed in
accordance with the internal laws of the State of New York.

 

  F.

Jurisdiction. The parties (i) submit to the jurisdiction of the courts of the
State of New York or the United States District Court for the Southern District
of New York for the purpose of any suit, action or other proceeding arising out
of or based upon this Agreement, (ii) agree not to commence any suit, action or
other proceeding arising out of or based upon this Agreement except the courts
of the State of New York or the United States District Court for the Southern
District of New York, and (iii) hereby waive, and agree not to assert, by way of
motion, as a defense, or otherwise, in any such suit,

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  action or proceeding, any claim that it is not subject personally to the
jurisdiction of the above-named courts, that its property is exempt or immune
from attachment or execution, that the suit, action or proceeding is brought in
an inconvenient forum, that the venue of the suit, action or proceeding is
improper or that this Agreement or the subject matter hereof may not be enforced
in or by such court.

 

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

[Signature page follows]

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IN WITNESS WHEREOF, the parties hereto have executed this Agreement to be
effective as of the date first set forth above.

 

COMPANY: PURE ACQUISITION CORP. By:  

/s/ Steven W. Tholen

  Name: Steven W. Tholen   Title: Chief Financial Officer PURCHASER: HIGHPEAK
PURE ACQUISITION, LLC By:  

/s/ Jack Hightower

  Name: Jack Hightower   Title: Chief Executive Officer

SIGNATURE PAGE TO PRIVATE PLACEMENT WARRANTS PURCHASE AGREEMENT