The digits form three 3-digit numbers reading left-to-right, and three 3-digit numbers reading top-to-bottom. Also consider these six 3-digit numbers reversed, that is, reading right-to-left and bottom-to-top.

For each of those nine digits, d, you count how many of the twelve 3-digit numbers are divisible by the number d. In the case of each d, that number, the count, is itself divisible by d.

How are the numbers arranged, with the understanding that rotations and reflections of that arrangement are possible alternatives?

If a number d is divisible by 5, it will end in 0 or 5.  Zero (0) is not available per the problem statement.  Any number to be divisible by five must rely on the 5.

If the 5 is place in the center - none of the twelve 3-digit numbers will be divisible by 5.

If the 5 is placed in the corner - two will be divisible by 5.

If the 5 is placed in the middle of a side - one number will be divisible by 5.

Count (5) = 0, 1, or 2.  Only 0 is divisible by 5.  Thus the 5 goes in the center.