16 HBr (aq) + 2 KMnO4 (aq) → 5 Br2 (aq) + 2 MnBr2 (aq) + 2 KBr (aq) + 8 H2O (l)
This is an oxidation-reduction (redox) reaction:
10 Br-I - 10 e- → 10 Br0 (oxidation)
2 MnVII + 10 e- → 2 MnII (reduction)
HBr is a reducing agent, KMnO4 is an oxidizing agent.