How many times do you need to enlarge each side of the square so that its perimeter increases 5 times?

Let us denote the length of the side of the original square by a.

Since the perimeter of any square is equal to the side length of this square multiplied by 4, the perimeter of this square is 4a.

If the sides of this square are increased so that the perimeter of the resulting square is increased by 5 times, then the perimeter of the resulting square will be 5 * 4a = 20a.

Then the side length of the resulting square will be 20a / 4 = 5a.

Therefore, in order for the perimeter of a square to increase by 5 times, the sides of this square must be increased by 5 times.

Answer: each side of the square needs to be increased 5 times.