[FORM OF AMENDMENT AGREEMENT] AMENDMENT AGREEMENT

Exhibit 10.5

[FORM OF AMENDMENT AGREEMENT]

AMENDMENT AGREEMENT

This Amendment Agreement (the “Agreement”), dated as of April     , 2012 (the “Effective Date”), is by and between Odyssey Marine Exploration, Inc., a Nevada corporation with offices located at 5215 W. Laurel Street, Tampa, Florida 33607 (the “Company”), and the holder identified on the signature page hereto (“Holder”).

R E C I T A L S

A. On or about November 8, 2011, the Company issued (i) $10,000,000 in aggregate principal amount of a senior convertible note (the “Initial Note”) and (ii) a warrant (the “Initial Warrants”) to purchase the Company’s common stock, $0.0001 par value per share (the “Common Stock”) pursuant to a Securities Purchase Agreement dated as of November 8, 2011 (the “Existing Securities Purchase Agreement”) to the Holder. Capitalized terms not defined herein shall have the meanings as set forth in the Existing Securities Purchase Agreement as amended hereby.

B. The Company and the Holder desire to enter into this Agreement, pursuant to which, among other things, the Company and the Holder shall amend certain of the Transaction Documents (as defined in the Existing Securities Purchase Agreement) and exhibits thereto.

A G R E E M E N T

1. Amendments.

1.1 Ratifications. Except as otherwise expressly provided herein, the Existing Securities Purchase Agreement and each other Transaction Document, is, and shall continue to be, in full force and effect and is hereby ratified and confirmed in all respects, except that on and after the Effective Date: (i) all references in the Existing Securities Purchase Agreement to “this Agreement”, “hereto”, “hereof”, “hereunder” or words of like import referring to the Existing Securities Purchase Agreement shall mean the Existing Securities Purchase Agreement as amended by this Agreement, (ii) all references in the other Transaction Documents, to the “Securities Purchase Agreement”, “thereto”, “thereof”, “thereunder” or words of like import referring to the Securities Purchase Agreement shall mean the Existing Securities Purchase Agreement as amended by this Agreement, (iii) all references in the Existing Registration Rights Agreement to “this Agreement”, “hereto”, “hereof”, “hereunder” or words of like import referring to the Existing Registration Rights Agreement shall mean the Existing Registration Rights Agreement as amended by this Agreement, and (iv) all references in the other Transaction Documents to the “Registration Rights Agreement”, “thereto”, “thereof”, “thereunder” or words of like import referring to the Registration Rights Agreement shall mean the Registration Rights Agreement as amended by this Agreement.

1.2 Amendments to the Existing Securities Purchase Agreement. As of the Effective Date:

(a) Recital D of the Existing Securities Purchase Agreement shall be amended and restated in its entirety to read as follows:

“Subject to the terms and conditions set forth in this Agreement, the Company may require the Buyers to participate in an Additional Closing (as defined below) for the purchase by the Buyers, and the sale by the Company, of up to that aggregate principal amount of Notes (each an “Additional Note”, and collectively, the “Additional Notes”) set forth opposite such Buyer’s name in column (4) on the Schedule of Buyers (which aggregate principal amount for all Buyers shall not exceed $8,000,000) (as converted, collectively, the “Additional Conversion Shares” and, collectively with the Initial Conversion Shares, the “Conversion Shares”).”

(b) The Schedule of Buyers attached to the Existing Securities Purchase Agreement is hereby amended and restated in its entirety in the form attached hereto as Schedule I (the “Revised Schedule of Buyers”) attached hereto. All references in the Transaction Documents to the Schedule of Buyers shall mean the Revised Schedule of Buyers.

1.3 Amendments to the Form of Additional Note. As of the Effective Date, the form of Additional Note to be delivered to the Holder on the Additional Closing Date is hereby amended and restated in its entirety as the form attached hereto as Exhibit A-2.

1.4 Amendments to Defined Terms as of Effective Date. As of the Effective Date, each of the Transaction Documents are hereby amended as follows:

(a) The defined term “Amendment Agreement” shall mean “that certain Amendment Agreement, dated as of April     , 2012, by and between the Company and the Buyer”.

(b) The defined term “Transaction Documents” is hereby amended to include the Amendment Agreement.

1.5 Amendments to Defined Terms as of Additional Closing Date. As of the Effective Date, each of the Transaction Documents are hereby amended as follows:

(a) The defined term “Schedule of Buyers” is hereby amended and restated as “the Revised Schedule of Buyers (as defined in the Amendment Agreement)”.

1.6 Amendment to Initial Note. As of the Additional Closing Date, the definition of Permitted Indebtedness in the Initial Note is hereby amended and restated as follows:

“Permitted Indebtedness” means (i) up to (x) an aggregate of $2 million of Indebtedness (but not including any Convertible Securities) owed to financial institutions and (y) an aggregate of $15 million of Project Finance Indebtedness (but not including any Convertible Securities) incurred by the Company or any of its Subsidiaries, in each case, that does not provide at any time for total interest and fees at a rate in excess of fifteen percent (15%) per annum (except, with respect to Project Finance Indebtedness with respect to a given project, to the extent such Project

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Finance Indebtedness is being paid off with cash flow being generated from such project), (ii) the Headquarters Indebtedness, (iii) the Permitted Senior Indebtedness, and (iv) Indebtedness evidenced by this Note and the Other Notes.

1.7 Amendment to Warrant. As of the Effective Date, Section 2 of the Warrant is hereby amended to add the following at the end:

(d) Number of Warrants. Upon any Additional Closing (as defined in the Securities Purchase Agreement), the number of shares of Common Stock issuable upon exercise of this Warrant shall be adjusted to the difference of (A) the greater of (x) the number of shares of Common Stock issuable upon exercise of this Warrant immediately prior to the Additional Closing Date (as defined in the Securities Purchase Agreement) and (y) the Maximum Eligibility Number immediately following the Additional Closing Date, less (B) such number of shares of Common Stock previously issued upon exercise of this Warrant prior to the Additional Closing Date.

2. Covenants.

2.1 Disclosure of Transactions and Other Material Information. On or before 9:30 a.m., New York time, on the first (1st) Business Day following the Effective Date, the Company shall file a Current Report on Form 8-K describing all the material terms of the transactions contemplated by the Agreements in the form required by the 1934 Act and attaching all the material Agreements (including, without limitation, this Agreement (and all schedules to this Agreement)) (including all attachments, the “8-K Filing”). From and after the issuance of the 8-K Filing, the Company shall have disclosed all material, non-public information (if any) delivered to any of the Holder by the Company or any of its Subsidiaries, or any of their respective officers, directors, employees or agents in connection with the transactions contemplated by the Agreements.

2.2 Fees. The Company shall reimburse Greenberg Traurig, LLP (counsel to the lead Holder), on demand, for all reasonable, documented costs and expenses incurred by it in connection with preparing and delivering this Agreement (including, without limitation, all reasonable, documented legal fees and disbursements in connection therewith, and due diligence in connection with the transactions contemplated thereby).

3. Miscellaneous. Section 9 of the Existing Securities Purchase Agreement (as amended hereby) is hereby incorporated by reference herein, mutatis mutandis.

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IN WITNESS WHEREOF, the parties hereto have executed this Agreement as of the day and year first above written.

[Amendment Agreement]

IN WITNESS WHEREOF, the parties hereto have executed this Agreement as of the day and year first above written.

SCHEDULE I

REVISED SCHEDULE OF BUYERS