A 13 foot ladder is placed 5 feet away from my wall. The distance from the ground straight up to the top of the wall is 13 foot. Will the ladder reach the top of the wall?

no

Step-by-step explanation:

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.