Human Cloning Ban Act of 2005 - Prohibits any person or private or public legal entity from: (1) conducting or attempting to conduct human cloning; (2) shipping the product of nuclear transplantation in interstate or foreign commerce for the purpose of human cloning; or (3) exporting to a foreign country an unfertilized blastocyst if such country does not prohibit human cloning. Sets forth criminal and civil penalties for violations.