Task Force 51 was a Starfleet task force extant in the late 24th century. It was part of the Starfleet Fifth Fleet.
In 2364, the Task Force was under the command of Admiral Bartholomew Thomas. Two of the ships deployed with the Task force included the Freedom-class USS Caravelle, and the Admiral's flagship, the Excelsior-class USS Joseph Kittinger. (Star Trek: Outpost)
In 2377-78, Admiral Chris Wallace was Task Force 51's commanding officer aboard the flagship USS Bright Star (a Galaxy (II) class large exploration cruiser commanded by Captain Nausicaà Miyazaki). Task Force 51, deployed on a mission of coreward exploration, was then homeported at Spacedock Nexus. (Ships of the Star Fleet, Vol. 4: Star Fleet Operating Forces. )