Soyuz TM-5 was the fifth cosmonaut-carrying spacecraft to visit the Russian Space Station Mir. It was launched on June 7, 1988, carrying the Mir EP-2 mission's three-person crew. This week-long stay on Mir occurred during the third long-duration Mir expedition, Mir EO-3. The crew of EP-2 returned to Earth aboard Soyuz TM-4, while the TM-5 spacecraft remained docked to Mir, acting as the lifeboat for the long-duration crew. On September 7, 1988, the TM-5 spacecraft undocked from Mir, and landed Mir EP-3 mission's two-person visiting crew. The de-orbit procedures for Soyuz were revised after this flight, as multiple issues almost prevented the descent module's safe de-orbit and landing.

Due to the Soyuz 33 failure, Bulgaria was the only East European Soviet ally not to have had a citizen visit a Soviet space station. Bulgarian Research Cosmonaut Aleksandr Aleksandrov used nearly 2,000 kg of equipment delivered by Progress freighters to conduct 46 experiments in the Shipka program during his stay.

46 scientific experiments were performed, including astrophysical and astronomical research using the Rozhen astronomical experiment, Earth observation (coast of the Black Sea region), materials sciences, medicine and biology. Photos and spectral analysis were taken from the Bulgarian territory, standard, when foreign cosmonauts are on-board the Mir. They also worked with the Kristallisator experiment.

On September 05, 1988 cosmonauts Vladimir Lyakhov and Abdulahad Momand undocked from Mir. They jettisoned the orbital module and made ready for deorbit burn to return to Earth. During descent, the spacecraft experienced a computer software problem combined with a sensor problem. This caused their landing to be delayed by a full day. The descent module, where they spent this 24-hour period, had no sanitary facilities. They would not have been able to redock with Mir because they had discarded the docking system along with the orbital module. Reentry occurred as normal on September 07, 1988. Following this incident, the Soviets decided that on future missions, they would retain the orbital module until after deorbit burn, as they had done on the Soyuz ferry flights