I don't how I can explain this in any simpler terms, the top equation is the manganate one,
1 Mole reacts with 5 electrons.
The last two equations show what the iron ethanedioate produces in terms of electrons, iron gives one and ethanedioate gives 2. This means for ONE mole of iron ethanedioate 3 electrons are produced. The Manganate needs 5 electrons to be reduced, at least for one mole of it.
The iron ethanedioate gives 3 electrons per mole. 3 and 5 are not equal.
Make them a common factor of 15, multiply the managante equation by 3 to get 15 electrons. Hence 3 moles of manganate
Multiply the iron ethandioate equation by 5 to get 15 electrons. Now the electrons are balanced, We have 3 moles of manganate and 5 of iron ethanedioate.
If it was 2:5 then this means we used two moles of Manganate, which is 10 electrons (2x5), and 5 moles of iron ethanedioate which produces 15 electrons (3x5). This is not an equal number of electrons