Square Poster, by definition of square, has equal base and height. Let's call it A. 

Poster Area = base x height = A x A

By the same logic, we can say that, for the sign ...

Sign Area = B x B

But, we know that the sides of the poster are 2 feet less than that of the sign.

Thus, A = B-2

We also know that the difference in areas is 5 square feet. Since the poster has smaller sides, it must be that the poster is the one with the smaller area. So, we know ...

(AxA) = (BxB)-5

by plugging in our equation for A, we get ...

(B-2)x(B-2) = (BxB)-5

multiplying out each side ...

B2-4B+4 = B2-5

Now we can gather like-terms. B2 cancels out, etc  ...

-4B = -9

B = 9/4

So, now we know the sides of the sign are each 9/4 feet.

Plugging this into our equation for A, we get ...

A = (9/4)-2 

A = (9/4)-(8/4)

A = 1/4

So, the sides of the poster are each 1/4 feet. Just to verify our answer, let's plug these in...

Poster Area = (1/4)x(1/4) = 1/16 square feet

Sign Area = (9/4)x(9/4) = 81/16 = 5+(1/16) square feet.

As we desired, the difference in areas is 5 square feet. So there's your answer! hope this helped.