The Illegal Border Crossers Reporting Act of 2005 - Directs the Secretary of Homeland Security to annually compile data on the following categories of information: (1) the number of unauthorized aliens who require medical care taken into custody by Border Patrol officials; (2) the number of unauthorized aliens with serious injuries or medical conditions Border Patrol officials refer to local hospitals or other health facilities; (3) the number of unauthorized aliens with serious injuries or medical conditions who arrive at U.S. ports of entry and subsequently are admitted into the United States for emergency medical care; (4) the number of unauthorized aliens described in clauses (2) and (3) who subsequently are taken into Department of Homeland Security (DHS) custody; and (5) a breakdown of the number of Mexicans and Other Than Mexicans described in clauses (1) through (3).