Family Education Reimbursement Act of 2005 - Directs the Secretary of Education to establish a Family Education Reimbursement Account Program for families of students displaced by Hurricane Katrina or Hurricane Rita.
Provides for reimbursing parents for costs of such students or preschool-age children attending schools or preschool programs, chosen by the parents, during the 2005–2006 school year.
Requires the Secretary to make a contract with a nongovernmental entity to administer and operate the program.