H.R.5740 - Federal Government - To amend title 38, United States Code, to establish a program of educational assistance for members of the Armed Forces who serve in the Armed Forces after September 11, 2001, and for other purposes.

Post-9/11 Veterans Educational Assistance Act of 2008 - Amends federal veterans' benefits provisions to entitle to educational assistance under the Montgomery GI Bill individuals in certain length-of-service categories who, commencing on or after September 11, 2001, serve on active duty in the Armed Forces.

Establishes the duration of such assistance (in most cases 36 months) and assistance amounts. Requires programs of education pursued with such assistance to be approved by the Secretary of Veterans Affairs. Allows for the pursuit of an approved program of education while on active duty. Allows, under such assistance, for the pursuit of: (1) programs on less than a half-time basis; (2) apprenticeship or other on-job training; (3) correspondence courses; (4) flight training; (5) tutorial assistance; and (6) licensure and certification tests. Makes individuals entitled to assistance under this Act also eligible for supplemental educational assistance for additional active duty service.

Requires the Secretary to carry out a program, to be known as the "Yellow Ribbon G.I. Education Enhancement Program," under which colleges and universities may enter into an agreement with the Secretary to cover, for certain individuals, a portion of established charges not otherwise covered and match contributions toward such costs.

Requires such educational assistance to be used within 15 years of the individual's discharge or release from active duty (with exceptions). Allows individuals currently under the Montgomery GI Bill educational assistance program to elect to participate in the post-9/11 educational assistance program with respect to any unused entitlement.