Iraq Contracting Fraud Review Act of 2005 - Directs The Secretary of Defense, acting through the Director of the Defense Contract Audit Agency, to review of each covered contract to determine if the contract has been the subject of fraud or any other contracting impropriety. Defines a covered contract as a contract or subcontract entered into on or after March 1, 2003, by the Department of Defense (DOD), if the contract or subcontract: (1) relates to reconstruction or troop support in Iraq; and (2) involves any contractor, subcontractor, or federal employee that has been indicted or convicted for fraud with respect to another DOD contract relating to such reconstruction or troop support in Iraq.