5 N2IO + 8 MnVIIO4- + 14 H+ 10 NVO3- + 8 (MnII)2+ + 7 H2O

This is an oxidation-reduction (redox) reaction:

8 MnVII + 40 e- 8 MnII (reduction)

10 NI - 40 e- 10 NV (oxidation)

Change the oxidation states