High rate sulfate reduction under acidic conditions opens possibilities for new process flow sheets that allow the selective recovery of metals from mining and metallurgical waste and process water. However, knowledge about high-rate sulfate reduction under acidic conditions is limited. This paper investigates sulfate reduction in a membrane bioreactor at a controlled pH of 5. Sulfate and formate were dosed using a pH-auxostat system while formate was converted into hydrogen, which was used for sulfate reduction. Sulfide was removed from the gas phase to prevent sulfide inhibition. This study shows a high-rate sulfate-reducing bioreactor system for the frrst time at pH 5, with a volumetric activity of 188 mmol $SO_4^{2-}$/I/d and a specific activity of 81 mmol $SO_4^{2-}$volatile suspended solids/d. The microbial community at the end of the reactor run consisted of a diverse mixed population including sulfate-reducing bacteria.