3 MnVIIO4- + 4 H+ + 5 NIIO 5 NVO3- + 3 (MnII)2+ + 2 H2O

This is an oxidation-reduction (redox) reaction:

3 MnVII + 15 e- 3 MnII (reduction)

5 NII - 15 e- 5 NV (oxidation)

Change the oxidation states