Fair Trade in Pouch Tuna Act of 2005 - Amends the Harmonized Tariff Schedule of the United States to eliminate tariffs on (thus providing duty-free treatment for) pouch tuna imported from member nations (except the Union of Myanmar) of the Association of Southeast Asian Nations (ASEAN) (Brunei, Cambodia, Indonesia, Laos, Malaysia, Philippines, Singapore, Thailand, and Vietnam). Limits the aggregate quantity of tuna entered during any calendar year to the quantity of such duty-free imports from beneficiary nations of the Andean Trade Promotion and Drug Eradication Act. Conditions eligibility on the provision and enforcement of internationally recognized worker rights and environmental protections.