5537 was the identification number assigned to a E-2T medical shuttle that was located on the Death Star. This vessel was labeled as a non-combatant, guaranteeing it would not be targeted by either the Rebel Alliance or the Galactic Empire.
During the events of the Battle of Yavin, Villian Dance, Teela Kaarz, Memah Roothes, Celot Ratua Dil, and Kornell Divini, who were defecting, seized control of the shuttle with the intention of fleeing the Death Star.
As the craft was nearing the limit of the station's tractor beams range, Darth Vader, piloting his TIE fighter, tried to intercept it. Nevertheless, he detected that the battle occurring in the Death Star's trench was of greater importance, and he reluctantly ceased his chase. Vader's attempt to catch them did give the tractor beam technicians the time needed to reactivate the tractor beam, and they did manage to capture the shuttle. Nevertheless, the station was obliterated within a few minutes, allowing the defectors to successfully escape.