Starbase 55 was a Federation starbase administered by Starfleet.
In 2364, the starship USS James Fennimore Cooper was at this starbase before its rendezvous with the USS Discovery. (TNG: "Conspiracy", okudagram)
Five years later, in 2369, this base was the destination of the USS Enterprise-D following the discovery of a Dyson sphere. (TNG: "Relics")