Preventing Sexual Assaults in the Military Act of 2005 - Authorizes necessary appropriations to: (1) eliminate the backlog in processing DNA evidence at military DNA laboratories, including the U.S. Army Criminal Investigation Laboratory; (2) ensure that DNA testing and analysis of samples from crimes, including sexual assault and other serious violent crimes, are carried out in a timely manner; (3) distribute a sufficient amount of DNA evidence kits to each military academy, domestic military base, overseas military base, and theater of operations; and (4) ensure that at least one military medical personnel member trained as a Sexual Assault Nurse Examiner (SANE) or Sexual Assault Forensic Examiner (SAFE) is on duty at all times in the health care facility of each military academy, domestic military military base, overseas military base, and theater of operations, except where a memorandum of understanding ensures that a nonmilitary SANE or SAFE is on duty at all times.