This question does not make much sense. In this sort of context, a square does not have two measures associated with it so either it is a 4 unit square or a 5 unit square but it cannot be a "4 and 5 by" square.
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perimeter of a square = 4 * root of the area. Perimeter = 4 * root 25 = 4 * 5 = 20 ft
Perimeter: 2(4+5) = 18 units Area: 4*5 = 20 square units
The area of similar figures is proportional to the square of any linear measurement. (And all linear measurements are directly proportional.) Thus, if the ratio of the perimeters is 5/4, the ratios of the lengths of sides is also 5/4. The ratio of the areas, on the other hand, is (5/4)2, so you can simply multiply the area of the smaller square by this factor.
5*4 = 20 square inches
The area of square is : 16.0