Military Families Leave Act of 2005 - Amends the Family and Medical Leave Act of 1993, and Federal law relating to the Armed Forces, to entitle eligible employees to certain leave because of any qualifying exigency arising out of the fact that their spouse, son, daughter, or parent is a member of the Armed Forces who is serving on active duty in support of a contingency operation or has been notified of an impending call or order to such active duty.