Why must the total increase in oxidation numbers equal the total decrease of them in redox reactions?
The reaction is with an advantage written in the simplified ion form:

$$\ce{5 Fe^2+ + MnO4- + 8 H+ -&gt; 5 Fe^3+ + Mn^2+ + 4 H2O}$$

Total oxidation numbers $+17=+17$

The oxidation number is formally the net charge an atom within a molecule would have held, if we had broken all bonds and bond electrons  had sticked to atoms according the atom electronegativity.

Therefore, the constant total sum of oxidation numbers across all involved atoms directly relates to the constant total sum of valence electrons and to the law of charge conservation.