H.R.5869: To authorize additional resources to identify and eliminate illicit sources of firearms smuggled into Mexico for use by violent drug trafficking organizations, and for other purposes.

Southwest Border Violence Reduction Act of 2008 - Directs the Attorney General to: (1) to expand resources for the Project Gunrunner initiative of the Bureau of Alcohol, Tobacco, Firearms, and Explosives (ATF) to identify, investigate, and prosecute firearms trafficking across the U.S.- Mexico border; and (2) provide ATF agents, equipment, and training to assist Mexican law enforcement officers in combating firearms trafficking and other criminal enterprises.