Conan Commemorative Coin Act This bill directs the Department of the Treasury to mint and issue up to 100,000 $5 gold coins and 350,000 $1 silver coins in commemoration of Conan, the military working dog of the U.S. Special Operations Forces who took part in the nighttime raid that resulted in the death of Abu Bakr al-Baghdadi, the leader of ISIS (the Islamic State of Iraq and Syria). All surcharges received by Treasury from sales of such coins shall be transferred to the Department of Veterans Affairs, where they may be used to provide additional funds for the service-dog veterinary-health benefit.