Orbital shuttle 5 was a Federation orbital shuttle that was in service with Starfleet from the late 23rd century to the mid-24th century, attached to the Earth Spacedock.
In 2286, orbital shuttle 5 was parked at a Starfleet facility near the Golden Gate Bridge. This shuttle was undergoing maintenance.
Soon after, orbital shuttle 5 was flying in the interior of the Spacedock when the Whale Probe passed by the space station. After the probe drained the energy from the station and from the ships within, this shuttle was without power and adrift.
Much later, orbital shuttle 5 was seen flying to the Spacedock. (Star Trek IV: The Voyage Home)
A year later, orbital shuttle 5 was seen again flying towards the Spacedock. (Star Trek V: The Final Frontier)
In 2364, orbital shuttle 5 was undergoing maintenance at a Starfleet facility near the Golden Gate Bridge. (TNG: "Conspiracy")
Apocryphal
Orbital shuttle 5 had been in service since the early 2270s. (Star Trek: Ships of the Line (2006), October; Star Trek: Ships of the Line (2010), December)