Assuming the wall makes a 90-degree angle with the ground, the ladder is the hypotenuse of a right triangle whose legs are the ground distance, the wall height, and whose hypotenuse is the ladder length.
The hypotenuse of a right triangle must be longer than either side. If one side is length 13 and one side is length 5, the hypotenuse must be about 13.93. A 13-ft ladder will not do.
