ladder leaning against the wall, touching the

wall at a height of 15 ft, its length is 5 feet

longer than its distance from the wall...

we build this visual image of a right triangle:

     |\

     | \

15 |  \ l

     |_  \

     |_|__\

    l-5  

we know that for a right triangle, a^2 + b^2 = c^2

   we have a = 15, b = l-5 and c = l

   15^2 + (l-5)^2 = l^2

   225 + l^2 - 10l + 25 = l^2

   250 - 10l = 0

   10l = 250

     l = 25

the ladder, then, is 20 feet from the wall