Catalyzes the conversion of deoxyribose 1-phosphate to deoxyribose 5-phosphate. Shows also weak activity with glucose 1-phosphate and mannose 1-phosphate. Could be involved in pentose biosynthesis. alpha-D-ribose 1-phosphate = D-ribose 5-phosphate 2-deoxy-alpha-D-ribose 1-phosphate = 2-deoxy-D-ribose 5-phosphate Can also use Ni(2+), Mn(2+) and Zn(2+), to a lower extent. kcat is 173 sec(-1) (at 90 degrees Celsius). Optimum pH is 7.5. Optimum temperature is 90 degrees Celsius. Homotetramer. Activated by phosphorylation. Belongs to the phosphohexose mutase family.