We have two squares. the ratio of the perimeter of the big square to the perimeter of the little square is 5:2. What is the ratio of the big square's area to the little square?
Let's assume that the side length of the big square is $5x$ and the side length of the small square is $2x$, where $x$ is a positive real number.
The perimeter of the big square is $4 \times 5x = 20x$, and the perimeter of the small square is $4 \times 2x = 8x$. Thus, the ratio of the perimeters is $20x : 8x = 5:2$.
The area of the big square is $(5x)^2 = 25x^2$, and the area of the small square is $(2x)^2 = 4x^2$. Therefore, the ratio of the areas is $25x^2 : 4x^2 = \boxed{\frac{25}{4}}$.