H.R.5737: To amend the Internal Revenue Code of 1986 to provide for a deduction for travel expenses to medical centers of the Department of Veterans Affairs in connection with examinations or treatments relating to service-connected disabilities.

Veterans Travel Tax Relief Act of 2008 - Amends the Internal Revenue Code to allow veterans a deduction from gross income for their travel expenses (e.g., transportation, food, and lodging) to a Department of Veterans Affairs medical center for treatment related to a service-connected disability or for an examination related to a claim for disability compensation or a pension.