The fifth dimension was the name applied to the realm of photonic lifeforms which were attacking Doctor Chaotica and his Fortress of Doom within The Adventures of Captain Proton holoprogram. The program was unable to realize that the photonic lifeforms were real, and actually came from a layer of subspace.
Tom Paris, as Captain Proton, received a message in his rocket ship stating that aliens from the fifth dimension were at war with Chaotica. (VOY: "Bride of Chaotica!")