2 KMnVIIO4 + 5 KNIIIO2 + 3 H2SO4 5 KNVO3 + K2SO4 + 2 MnIISO4 + 3 H2O

This is an oxidation-reduction (redox) reaction:

2 MnVII + 10 e- 2 MnII (reduction)

5 NIII - 10 e- 5 NV (oxidation)

Change the oxidation states