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To find the height above the ground where the ladder meets the wall, we can use the Pythagorean theorem.
Let x be the height above the ground the ladder meets the wall.
According to the information given, the ladder (13m) is the hypotenuse, the base of the ladder is 5m, and the height we are solving for is x.
Using the Pythagorean theorem:
(5)^2 + x^2 = (13)^2
25 + x^2 = 169
x^2 = 144
x = 12
Therefore, the height above the ground where the ladder meets the wall is 12m.
So, the answer is C. 12 m.