Soyuz 5 was piloted by commander Boris Volynov and carried flight engineers Aleksei Yeliseyev and Yevgeny Khrunov as the crew to be transferred to Soyuz 4 for reentry. The mission plan contained scientific, technical, and medical-biological research, testing of spacecraft systems and design elements, docking of piloted spacecraft, and transfer of cosmonauts from one craft to another in orbit.

Volynov remained behind on Soyuz 5, and returned to Earth in a remarkable re-entry. The service module of the Soyuz failed to separate after retrofire, but by that point it was too late to abort. While this had occurred on various Vostok and Voskhod flights, it was a much more serious problem for Volynov, as the Soyuz service module was much larger than the small retropack the earlier vehicles employed.

When the Soyuz started aerobraking in the upper reaches of the atmosphere, the combined spacecraft sought the most aerodynamically stable position - nose forward, with the heavy descent module facing directly into the air stream with only its light metal entry hatch at the front to protect it. The gaskets sealing the hatch began to burn, filling the compartment with dangerous fumes and smoke. The deceleration, while normal for reentry, pulled Volynov outward against his harness rather than against the padded seat. As the thermal and aerodynamic stresses on the combined craft increased, struts between the descent and service modules broke off or burned through before the hatch failed. The descent module immediately righted itself once the service module was gone, with the heat shield forward to take the brunt of re-entry.

There was one final problem in store for Volynov when the parachute cables partially tangled and the soft-landing rockets failed, resulting in a hard impact which broke some of his teeth. The capsule came down in the Ural Mountains at 200 km (120 mi) of the southwest of Kostanay, near Orenburg, Soviet Union, far short of its target landing site in Kazakhstan. The local temperature was −38 °C (−36 °F), and knowing that it would be many hours before rescue teams could reach him, Volynov abandoned the capsule and walked for several kilometers to find shelter at a local peasant's house. It would be seven years until Volynov flew again, on Soyuz 21.

A similar incident occurred decades later with Soyuz TMA-11 on 19 April 2008, though the latter's landing was not as rough.