J.R. S. answered 02/14/21
Ph.D. University Professor with 10+ years Tutoring Experience
First, remember that O has an oxidation of 2- (except in peroxides when it is 1), and H has an oxidation number of 1+ (except in hydrides when it is 1-). In this problem you don't need to worry about H.
Looking at MnO4-
We know that O has an oxidation number of 2-, so what does Mn have to be so that the overall charge is 1-?
There are 4 oxygens for a total of -8 so Mn would have to be +7 in MnO4-.
Looking at Mn2+, we see that Mn has an oxidation number of 2+
So, Mn went from 7+ to 2+ which means it gained 5 electrons