Spoiler warning: Plot and/or ending details follow.
In the late 2140s decade, a major conference regarding the future of human spaceflight was held at the base. At the conference, Doctor Milton Kornheiser stated that warp factor 4 would be the fastest speed that any warp capable vessel would be able to achieve. (ST reference: Spaceflight Chronology)
In 2257, Lieutenant Spock, serving as science officer of the USS Enterprise under Captain Christopher Pike, had himself committed to the psychiatric facility at Starbase 5 while on extended leave from his duties. (DSC episode: "New Eden")
Commander Samir al-Halak traveled to Starbase 5 in 2336 on his way to Farius Prime, rather than making a planned trip to Betazed to meet with his lover, Anisar Batra. Batra eventually tracked Halak to the starbase. (TLE novel: Well of Souls)