Starbase 185 was a Federation starbase facility which was in operation in the late 24th century. It was located in the Iota Leonis star system, which was around 7,000 light years from System J-25. (TNG episode: "Q Who"; TTN novel: Fallen Gods)
The USS Enterprise was transported to System J-25 in 2365. At this point, Starbase 185 was the closest starbase to the Enterprise's position (a maximum warp trip of "two years, seven months, three days, eighteen hours"). (TNG episode: "Q Who")
In the late 2370s and early 2380s, the starbase was under the command of Admiral Alita de la Fuego. (TTN novel: Taking Wing)
In late 2379, the USS Titan was due to stop off at the base after departing from the Utopia Planitia Fleet Yards. Unfortunately, the medical relief mission to Romulus delayed the starship arrival.
Doctor Xin Ra-Havreii was hoping to be able to secure a fresh supply of real levithi nuts on the base, but the delay meant that he had to acquire another supply. (TTN novel: Taking Wing)
Captain Jean-Luc Picard contacted the starbase in 2380 to inform Starfleet Command of Q's appearance. (TNG novel: Q & A)
In 2381, the starbase was under the command of Captain Jax Dreshing when the former Borg drone Axum arrived at the station seeking medical attention. (VOY novel: Protectors)
In 2382, Admiral de la Fuego conducted holoconferences from her office at Starbase 185 with Captain Riker and Fleet Admiral Akaar with the assistance of her aide, a Lieutenant named Jenny. (TTN novel: Fallen Gods)