G.I. Bill Enhancement Act of 2005 - Exempts members of the Armed Forces and Selected Reserve on active duty between November 16, 2001, and the termination date of Executive Order 13235 from the mandatory payroll deductions ($100 for the first 12 months of active duty pay) under the veterans' basic educational assistance program. Provides for reimbursement of payroll deductions taken prior to the enactment of this Act. Allows such members to withdraw an election not to receive basic educational assistance.