Airport Emergency Reimbursement Act of 2005 - Amends federal aviation law to provide a credit to an owner or operator of an airport that allows the Director of the Federal Emergency Management Agency (FEMA) or the head of a state or local agency to utilize the airport to respond to a disaster or emergency. Allows application of such credit toward the non-federal share of allowable costs for projects under the airport improvement program. Requires such credit to equal the revenues the airport lost, including operational costs incurred by the owner or operator, during the period of such utilization.