The fifth dimension was the name applied by Doctor Chaotica to the trans-dimensional realm of photonic lifeforms who visited the holodeck of USS Voyager in 2375.
Tom Paris, as Captain Proton in the holodeck program The Adventures of Captain Proton received a telegram in his rocket ship stating that aliens from the fifth dimension were at war with Chaotica and his Fortress of Doom within the holoprogram. The program was unable to realize that the photonic lifeforms were real and actually came from a trans-dimensional realm. (VOY: "Bride of Chaotica!")
According to Chaotica, there were only five dimensions. (VOY: "Shattered")