An elementary math problem

Long time ago, I created a table-based problem which requires technique of invariant to be solved. I’m pretty sure that my solution (at that time) was only about a way to assign weights to squares in the table. Unfortunately, I have no idea what the weights are.

Anyway, here is the problem, hope you’ll enjoy solving it.

Given a $50 \times 50$ square table containing exactly one number in each unit square. All unit squares contain number 0 except the top left unit square contains number 1. In each move, either a $2 \times 2$ sub-square or a $3 \times 3$ sub-square of the table is chosen and then each number inside the sub-square reduces by 1 unit. Is it possible for all 2500 numbers in the table become multiples of 5 after a finite number of moves?