American Veterans Homeownership Act of 2005 - Amends the Internal Revenue Code to: (1) revise the definition of qualified veteran for purposes of the veterans' mortgage bond program to include all veterans who served on active duty regardless of date of service; (2) allow veterans to apply for financing under such bond program up to 25 years after the end of their active duty; and (3) revise volume limitations applicable to the issuance of such bonds in certain states.