Captain Jean-Luc Picard went there in 2365 to undergo a cardiac replacement. Wesley Crusher took his Academy entrance exams there at the same time. When Picard's operation required Doctor Katherine Pulaski, the USS Enterprise-D made an unscheduled stop. (TNG: "Samaritan Snare")
In 2367, while trying to survive on Lambda Paz, Wesley asked Picard if he remembered the trip they took together to this base. Wesley felt that Picard had opened up to him and, in the process, he had come to know more about the captain. (TNG: "Final Mission")
In 2369, Geordi La Forge, when investigating the murder of Lieutenant Keith Rocha, requested a display of the personal records of the lieutenant from the Relay Station 47 computer for stardates 46455 to 46460. One of these records mentioned this starbase.
In the log entry, Rocha wrote, "Heavy load today. Starfleet Command requested 20 new lines between Starbase 515 and Sector 32834. Apparently in support of expanded exploratory ops. The only problem is that we've already promised those lines to Admiral Taylor." (TNG: "Aquiel", display graphic)
Starbase 515 offered biomedical and health care services in a medical facility.
- 03-1442 Vulcan Physiology Unit
- 03-1444 Exobiology Research Division
- 03-1452 Surgical Suite 3 (Cardiac)
- 03-1453 Surgical Suite 4 (Bionic)
- 03-1457 Surgical Suite 5 (General)
- 03-1459 Surgical Suite 6 (Cryo)
- 03-1473 Zero Gravity Therapy Ward
- 03-1480 Biomedical Imaging Services
- 03-1482 Andor Environment Ward
- 03-1483 Conference room 4
- 03-1484 Conference room 5
- 03-1493 Kei/Yuri Therapy Unit
- 03-1502 Robert McCullough, MD
- 03-1507 Les Landau, MD, DGA
- 03-1520 Robert Metoyer, MD, DGA
- 03-1522 Sam Freedle, MD, DGA
- 03-1523 Adele Simmons, MD, DGA
- 03-1524 Scott Luhrsen, MD, DGA
- 03-1525 Brian Faul, MD, DGA
According to the Star Trek Encyclopedia (3rd ed., p. 466), after "The Neutral Zone" had aired, where Starbase 718 was mentioned in dialogue, it was decided that the starbase numbers shouldn't go much higher than 500.
According to StarTrek.com, the Star Trek Encyclopedia (4th ed., vol. 2, p. 318), and the third season edition of the Star Trek: The Next Generation Writers' Technical Manual (p. 16), Starbase 515 was located in the Scylla sector. The script for this episode identifies the starbase as Starbase Scylla 515. 
For the remastered episode "Aquiel", the log entry stardate was changed from 46457 to 45457. The log entry, with the starbase's name, was new to the episode, having replaced the pre-remastered entry.