Exhibit 10.5

Mr. David F. Hale 17079 Circa Del Sur Rancho Santa Fe, California 92067 March 10, 2011

Re: Position as Executive Chairman of the Board of Directors of Biocept, Inc.

Dear David:

It is my sincere pleasure, on behalf of Biocept, Inc. (“Biocept”), to offer you the role of Executive Chairman of the Board of Directors of Biocept (the “Board”). Should you choose to accept this offer on the terms provided herein, your appointment as Executive Chairman of the Board is contingent and effective upon your execution of this letter. The term of your appointment as the Executive Chairman shall be from the date of your execution of this letter through December 31, 2013 (the “Term”), unless earlier terminated due to your resignation or removal from the Board.

As Executive Chairman, you will be expected to work closely with the Board and the executive team of Biocept to further the goals and objectives of the organization, consistent with the usual and customary duties of an executive chairman of the board of a biotechnology company. The Board expects that in your role as Executive Chairman, you will initially maintain an office at Biocept’s San Diego, California headquarters, be involved in the day-to-day high level management decisions as guided by the Board, serve as a facilitator of communications between the senior management team of Biocept and the non-employee directors, and spend an amount of time at Biocept commensurate with your duties and level of compensation set forth below. In addition, you have agreed that, during your tenure as Executive Chairman of Biocept, you will promptly notify the Board if you accept employment as an executive officer of any other company or organization. The Board, in its sole discretion, will determine whether any such employment is consistent with the duties undertaken pursuant to this letter.

As compensation for your services as Executive Chairman, during your service as Executive Chairman and retroactive to January 1, 2011, you will be paid an Executive Chairman fee of (a) $25,000 per month for each month prior to the appointment by the Board of a new Chief Executive Officer (“CEO”) and for each of the three months following the appointment of the new CEO, and (b) $12,500 per month for each month commencing with the fourth month following the appointment of the new CEO (collectively, the “Chairman Fees”), which such fees shall be payable, less any required payroll deductions and withholdings, in regular periodic payments in accordance with Biocept policy. In the event that you are removed from the Board without Cause (as defined in Biocept’s 2007 Equity Incentive Plan (the “Plan”)), you will continue to receive the applicable Chairman Fees for the remainder of the Term, subject to your furnishing to Biocept an effective waiver and release of claims in a form specified by Biocept and consistent with standard practices.

As additional compensation, contingent and effective upon the commencement of your services to Biocept, you will receive the following equity grants:

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(1) Biocept will grant to you an option (the “Option”) under the Plan to purchase 428,597 shares of Biocept’s common stock (the “Common Stock”) which shall vest in equal monthly installments over the four year period beginning on January 1, 2011. The Option will be early exercisable at your option and will fully vest upon a Change in Control (as defined in the Plan) or an underwritten initial public offering of the Common Stock (“IPO”) occurring before the Option is fully vested and during your Continuous Service (as defined in the Plan). In the event that your Continuous Service (as defined in the Plan) is involuntarily terminated by the Company or its shareholders without Cause (as defined in the Plan), the Option will fully vest, subject to your furnishing to Biocept an effective waiver and release of claims in a form specified by Biocept and consistent with standard practices. You agree that you may, at your sole discretion, early exercise the Option in full within a reasonable time period following your execution of this letter. The exercise price of the Option shall be the fair market value as of the date of grant, as determined by the Board. Additionally, if (i) Biocept issues and sells shares of its equity securities to investors in an equity financing (such shares sold in such financing, the “Next Equity Securities”), (ii) you are providing Continuous Service (as defined in the Plan) immediately following the sale of the Next Equity Securities, and (iii) the number of shares subject to the Option represent less than 1% of Biocept’s capitalization on a fully-diluted basis (assuming the exercise of all outstanding warrants and stock options and the unallocated pool of stock awards available for future issuance under the Plan) following such sale of Next Equity Securities, then Biocept shall grant you an additional stock option such that the number of shares subject to such additional stock option will, when added to the number of shares subject to the Option, result in stock option grants to you covering a number of shares equal to 1% of Biocept’s capitalization on a fully-diluted basis (assuming the exercise of all outstanding warrants and stock options and the unallocated pool of stock awards available for future issuance under the Plan) following such sale of Next Equity Securities, which such additional stock options shall have (a) the same vesting terms as the Option, (b) the same vesting commencement date as the Option and (c) an exercise price equal to the fair market value as of the date of grant, as determined by the Board (such right to receive an additional stock option grant, the “True-Up Right”). The foregoing True-Up Rights shall terminate upon Biocept’s receipt of aggregate proceeds of $15,000,000 or more (the “Threshold”) from the sale of Next Equity Securities, excluding the conversion of any outstanding indebtedness. Notwithstanding the foregoing and for purposes of clarity, the True-Up Rights shall apply with respect to the total amount of equity securities sold in the last sale of Next Equity Securities that results in the Threshold being exceeded;

(2) Biocept will grant you a time-based restricted stock unit award (the “Time-Based RSU Award”) of up to 428,597 shares of Biocept’s Series BB Preferred Stock (the “Series BB Preferred”). Under the Time-Based RSU Award, upon a Change in Control (as defined in the Plan) or IPO occurring during your Continuous Service (as defined in the Plan), all 428,597 shares of Series BB Preferred subject to the Time-Based RSU Award shall fully vest and be issued to you upon such event. In addition, if a Change in Control (as defined in the Plan) or IPO occurs within 10 years of January 1, 2011 but after the involuntary termination of your Continuous Service (as defined in the Plan), a portion of the shares of Series BB Preferred subject to the Time-Based RSU Award will vest and be issued to you based upon the number of months you provided Continuous Service (as defined in the Plan) divided by 48, such portion not to exceed the full 428,597 shares subject to the Time-Based RSU Award; provided, that in the event such involuntary termination of Continuous Service (as defined in the Plan) was without

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Cause (as defined in the Plan) and you furnished Biocept an effective waiver and release of claims in a form specified by Biocept and consistent with standard practices, the full 428,597 shares subject to the Time-Based RSU Award will vest and be issued to you; and

(3) Biocept will grant you a performance-based restricted stock unit award (the “Performance RSU Award”) for shares of Series BB Preferred. Under the Performance RSU Award, upon a Change in Control (as defined in the Plan) or IPO (a “Vesting Event”) occurring within 10 years of January 1, 2011, a portion of shares of Series BB Preferred subject to the Performance RSU Award shall vest and be issued to you based upon achievement of the following Milestones (as defined below) prior to such Vesting Event as set forth below; provided, that in the event your Continuous Service (as defined in the Plan) is involuntary terminated by the Company or its shareholders without Cause (as defined in the Plan) prior to the Vesting Event but before all of the Milestones have been achieved, and you furnished Biocept an effective waiver and release of claims in a form specified by Biocept and consistent with standard practices, then (i) for each Milestone that has been achieved, a number of shares of Series BB Preferred equal to that set forth below for the applicable Milestone shall vest and (ii) for each Milestone that has not been achieved, a number of shares of Series BB Preferred equal to 0.5% of Biocept’s capitalization on a fully-diluted basis immediately prior to the Vesting Event (assuming the exercise of all outstanding warrants and stock options and the unallocated pool of stock awards available for future issuance under the Plan) shall vest upon such Vesting Event. If, during your Continuous Service (as defined in the Plan) and prior to the Vesting Event, there has been commercial acceptance of Biocept’s OncoCEE-BR^TM test, as determined by the Board in good faith (the “Commercial Milestone”), then a number of shares of Series BB Preferred equal to 0.5% of Biocept’s capitalization on a fully-diluted basis immediately following achievement of the Commercial Milestone (assuming the exercise of all outstanding warrants and stock options and the unallocated pool of stock awards available for future issuance under the Plan) shall vest upon such Vesting Event. If, during your Continuous Service (as defined in the Plan) and prior to the Vesting Event, Biocept has received an aggregate of at least $15,000,000 in new funds from: (a) the sale of Biocept’s securities to one or more outside investors who are not currently shareholders of Biocept; (b) third party collaborators or partners; and/or (c) grant, debt or other non-dilutive funding from third parties (the “Funding Milestone”), then a number of shares of Series BB Preferred equal to 0.5% of Biocept’s capitalization on a fully-diluted basis immediately following achievement of the Funding Milestone (assuming the exercise of all outstanding warrants and stock options and the unallocated pool of stock awards available for future issuance under the Plan) shall vest upon such Vesting Event. If, during your Continuous Service (as defined in the Plan) and prior to the Vesting Event, all of the following objectives have been achieved, as determined by the Board in good faith (the “Leadership Milestone,” and collectively with the Commercial Milestone and the Funding Milestone, the “Milestones”):

• Implementation of a change in the culture of Biocept from research to business;

• Hiring of a new CEO approved by the Board;

• Development of a two-year operating plan and a five-year strategic plan, each of which is approved by the Board;

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• Restructuring of the Board to support financing and long term growth;

• Completion and presentation to the Board of an assessment of Biocept’s senior management team and implementation of any changes that need to be made following such assessment that are approved by the Board;

• Development and presentation to the Board of a plan for establishing the clinical value of circulating tumor cells (“CTCs”) in the treatment of patients with cancer and implementation of the plan following approval by the Board;

• Development of an overall branding program for Biocept’s core business that is approved by the Board;

• Development of corporate objectives for 2011 that are approved by the Board; and

• Establishment of Biocept as the premiere partner of the Bio-Pharma industry in performing CTC tests for clinical trials;

then a number of shares of Series BB Preferred equal to 0.5% of Biocept’s capitalization on a fully-diluted basis immediately following achievement of the Leadership Milestone (assuming the exercise of all outstanding warrants and stock options and the unallocated pool of stock awards available for future issuance under the Plan) shall vest upon such Vesting Event. In addition, if a Vesting Event occurs during your Continuous Service, but before all of the Milestones have been achieved, then (i) for each Milestone that has been achieved, a number of shares of Series BB Preferred equal to that set forth above for the applicable Milestone shall vest and (ii) for each Milestone that has not been achieved, a number of shares of Series BB Preferred equal to 0.5% of Biocept’s capitalization on a fully-diluted basis immediately prior to the Vesting Event (assuming the exercise of all outstanding warrants and stock options and the unallocated pool of stock awards available for future issuance under the Plan) shall vest upon such Vesting Event.

Biocept will also reimburse you for reasonable out-of-pocket expenses incurred in connection with your service as a director in accordance with Biocept’s established reimbursement policies. You will also receive indemnification under Biocept’s standard form of indemnity agreement for directors.

This letter, along with the documentation reflecting the equity grants referred to herein, constitutes the entire agreement between you and Biocept regarding the subject matter hereof. This agreement supersedes any other agreements or promises made to you by anyone, whether oral or written, and it may only be modified in a writing signed by a duly authorized officer of Biocept.

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If the terms of this letter are acceptable to you, please sign and date this letter below and return it to me in the enclosed return envelope, retaining a copy for your records.

Very truly yours,

/s/ M. Faye Wilson

M. Faye Wilson

Lead Independent Director

Biocept, Inc.

Accepted and agreed:

/s/ David F. Hale

David F. Hale

Date: March 10, 2011

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