Rural Teacher Retention Act of 2005 - Directs the Secretary of Education to carry out a five-year pilot program of making allotments to applicant rural local educational agencies for: (1) one-time signing bonuses of up to $2,000 for teachers who begin employment with them on or after enactment of this Act; and (2) bonuses of up to $3,000 to qualified teachers who work in them for at least three consecutive years (or nonconsecutive years under certain circumstances).