The rectangle is cut into several rectangles, the perimeter of each of which is divisible by 5

The rectangle is cut into several rectangles, the perimeter of each of which is divisible by 5. Is it true that the perimeter of the starting rectangle is also divisible by 5?

Since the perimeter of each rectangle is divisible by 5, no matter how many rectangles there are, their total perimeter will ALWAYS be divisible by 5, because the sum of their perimeters will end in 0 or 5.
For example, a large rectangle is cut into 4 small ones. The perimeter of each small rectangle is 25, then the perimeter of the large rectangle is 100. Both 25 and 100 are divisible by 5.
The answer is yes, that’s right.