The Alpha V colony (also known as Colony 5 or Earth colony 5) was a Federation colony located on planet, Alpha V, located in the Alpha system. In 2266, relatives of Charles Evans resided in the colony.
After escaping from Thasus, Evans very much wanted to make it to the colony and used his psionic powers to assume control of the USS Enterprise when Captain James T. Kirk grew concerned at Charlie's powers and attempted to keep the ship away from the colony. It was only the Thasians intervention that prevented Charlie and the Enterprise from reaching the colony. (TOS episode & novelization: Charlie X)