The Starfleet base where Jean-Luc Picard went for a risky procedure on his artificial heart in 2365.
Starbase 515 was a Starfleet starbase with an advanced medical facility. In 2365 Jean-Luc Picard travelled there by shuttle, accompanied by Wesley Crusher, for a procedure to replace his artificial heart, which he had needed since being stabbed in his youth.
The surgery went wrong, and Katherine Pulaski had to be brought from the Enterprise-D to save him. During the shuttle trip Picard told Wesley how he had lost his heart in a fight with Nausicaans as a brash young officer, a story he had long kept private.