AMENDMENT NUMBER THREE to the Amended and Restated Letter Agreement dated as of October 1, 2004 by and among NEW CENTURY MORTGAGE CORPORATION NC CAPITAL CORPORATION

Exhibit 10.5

AMENDMENT NUMBER THREE

to the

Amended and Restated Letter Agreement

dated as of October 1, 2004

by and among

NEW CENTURY MORTGAGE CORPORATION

NC CAPITAL CORPORATION

NEW CENTURY CREDIT CORPORATION

and

CITIGROUP GLOBAL MARKETS REALTY CORP.

This AMENDMENT NUMBER THREE (this “Amendment Number Three”) is made this 29^th day of December, 2004, among NEW CENTURY MORTGAGE CORPORATION, having an address at 18400 Von Karman, Suite 1000, Irvine, California 92612 (“NC Mortgage”), NC CAPITAL CORPORATION, having an address at 18400 Von Karman, Suite 1000, Irvine, California 92612 (“NC Capital”), NEW CENTURY CREDIT CORPORATION, having an address at 18400 Von Karman, Suite 1000, Irvine, California 92612 (“NC Credit”) and CITIGROUP GLOBAL MARKETS REALTY CORP., having an address at 390 Greenwich Street, New York, New York 10013 (“Citigroup”) to the AMENDED & RESTATED LETTER AGREEMENT, dated as of October 1, 2004, among NC Mortgage, NC Capital, NC Credit and Citigroup, as amended (the “Letter Agreement”).

RECITALS

WHEREAS, NC Mortgage, NC Capital and NC Credit have requested that Citigroup agree to extend the termination date as more expressly set forth below and Citigroup has agreed to such request.

WHEREAS, as of the date of this Amendment Number Three, each of NC Mortgage, NC Capital and NC Credit represents to Citigroup that it is in compliance with all of the representations and warranties and all of the affirmative and negative covenants set forth in the Letter Agreement and the Amended and Restated Purchase and Sale Agreement, dated as of October 1, 2004, among NC Capital, NC Credit and Citigroup (the “Purchase and Sale Agreement”) and is not in default under the Letter Agreement or the Purchase and Sale Agreement.

NOW THEREFORE, for good and valuable consideration, the receipt and sufficiency of which are hereby acknowledged, and of the mutual covenants herein contained, the parties hereto hereby agree as follows:

SECTION 1. Effective as of December 29, 2004, the first paragraph of Section 1(a) of the Letter Agreement is hereby amended by deleting the words “December 31, 2004” on the second and third lines thereof and replacing each with “March 31, 2005”.

SECTION 2. Effective as of December 29, 2004, the first paragraph of Section 4(c) of the Letter Agreement is hereby amended by deleting the words “December 31, 2004” on the second and third lines thereof and replacing each with “March 31, 2005”.

SECTION 3. Fees and Expenses. NC Capital agrees to pay to Citigroup all fees and out of pocket expenses incurred by Citigroup in connection with this Amendment Number Three (including all reasonable fees and out of pocket costs and expenses of Citigroup’s legal counsel incurred in connection with this Amendment Number Three), in accordance with Section 5(i) of the Letter Agreement.

SECTION 4. Defined Terms. Any terms capitalized but not otherwise defined herein shall have the respective meanings set forth in the Letter Agreement.

SECTION 5. Representations. In order to induce Citigroup to execute and deliver this Amendment Number Three, NC Capital, NC Mortgage and NC Credit hereby represent to Citigroup that as of the date hereof, after giving effect to this Amendment Number Three, each of NC Capital, NC Mortgage and NC Credit is in full compliance with all of the terms and conditions of the Letter Agreement and the Purchase and Sale Agreement and no Termination Event or material adverse change has occurred under the Letter Agreement and no Seller default or Seller Event of Default has occurred under the Purchase and Sale Agreement.

SECTION 6. Limited Effect. This Amendment Number Three shall become effective upon the execution hereof by the parties hereto. Except as expressly amended and modified by this Amendment Number Three, the Letter Agreement shall continue in full force and effect in accordance with its terms. Reference to this Amendment Number Three need not be made in the Letter Agreement or any other instrument or document executed in connection therewith, or in any certificate, letter or communication issued or made pursuant to, or with respect to, the Letter Agreement, any reference in any of such items to the Letter Agreement being sufficient to refer to the Letter Agreement as amended hereby.

SECTION 7. GOVERNING LAW. THIS AMENDMENT NUMBER THREE SHALL BE CONSTRUED IN ACCORDANCE WITH THE LAWS OF THE STATE OF NEW YORK AND THE OBLIGATIONS, RIGHTS, AND REMEDIES OF THE PARTIES HEREUNDER SHALL BE DETERMINED IN ACCORDANCE WITH SUCH LAWS WITHOUT REGARD TO CONFLICT OF LAWS DOCTRINE APPLIED IN SUCH STATE (OTHER THAN SECTION 5-1401 OF THE NEW YORK GENERAL OBLIGATIONS LAW).

SECTION 8. Counterparts. This Amendment Number Three may be executed by each of the parties hereto on any number of separate counterparts, each of which shall be an original and all of which taken together shall constitute one and the same instrument.

[SIGNATURE PAGE FOLLOWS]

-2-

IN WITNESS WHEREOF, NC Capital, NC Mortgage, NC Credit and Citigroup have caused this Amendment Number Three to be executed and delivered by their duly authorized officers as of the day and year first above written.

-3-