What you have described is a right angled triangle with a hypotenuse of length 13 feet and a base of 5 feet. To find the length of the remaining side (i.e. how far up the side of the building the ladder reaches) you have to use Pythagora's Theorem. This states that the hypotenuse squared is equal to the sum of the squares of the other two sides. So your answer should be 13^2=5^2+(how far up the side of the building the ladder reaches)^2, which becomes 169=25+(other side)^2, =169-25=(other side)^2 = 144= (other side)^2, so the height that the ladder reaches up the side of the building equals 12 feet.
