Teague Ryan Sudden Child Cardiac Arrhythmia Syndromes Screening and Education Act of 2005 - Amends the Public Health Service Act to require the Secretary of Health and Human Services, acting through the Director of the Centers for Disease Control and Prevention (CDC), to award grants or contracts to carry out programs to: (1) screen children for sudden cardiac arrhythmia syndromes; (2) provide referrals for medical services regarding such syndromes; and (3) provide education on such syndromes to health professionals and the general public. Requires the Secretary to give priority to: (1) screenings and referrals for children who participate, or intend to participate, in organized sports; and (2) educational activities directed toward parents of such children and health professionals who commonly provide medical care for such children.