What value of c makes x^2 +5x+c a perfect square.

To find a perfect square, all you need to do is divide the second coefficient by 2 (5 in this case) and then square it. In other words:

5/2=2.52. 5^2=6.25. Thus, x^2+5+6.25, and in factored form, (x+2.5)(x+2.5)

Hope this helps!