It can't be explained. Can you explain why we are ' at the library' when we are inside? Why are we 'in a car' but 'on a plane/train'? Why can we say both 'at the beach' and 'on the beach' with little to no difference in meaning?
It's just how prepositions work. That's the only explanation you will ever get from anyone.
But surely someone might explain the intention of på. Is it four 'in every' five years? Or should you think of it as 'on the period'? In dutch the equivalent of på may in cases be translated to per.
You be anyone, methinks for meself.
Also note that to explain means to clarify. A single word can sometimes explain a universe of thought.