If the ratio of the corresponding side length of two similar polygons is 5:9 which is the ratio of their perimeters

The ratio of their perimeters would also be 5:9.

To prove this assume one triangle has lengths 5x, 5x, and 5x. That means the other triangle would have 9x, 9x, and 9x. If you add up the lengths of the first triangle you would get 15x and if you add up the lengths of the second triangle you would get 27x. Let's put that in ratio form:

15x : 27x

divide both sides by x

15:27

divide both sides by 3

5:9