Starbase 55 was a Federation starbase administered by Starfleet in the late 24th century.
In 2364, prior to stardate 41044.2, the starship USS James Fennimore Cooper had a stay at this starbase before its rendezvous with the USS Discovery. (TNG: "Conspiracy")
Five years later, in 2369, It was the destination of the USS Enterprise-D following the discovery of a Dyson sphere. (TNG: "Relics")