Given a right triangle where the length of the adjacent side is 5 and the hypotenuse is 13, calculate the cosine of the angle adjacent to the adjacent side.

To find the cosine of the angle adjacent to the adjacent side in a right triangle, you can use the cosine formula: \[ \cos(A) = \frac{\text{adjacent side}}{\text{hypotenuse}}. \] In this case, the length of the adjacent side is 5 and the length of the hypotenuse is 13. Plugging in these values gives: \[ \cos(A) = \frac{5}{13}. \] So, the cosine of the angle adjacent to the adjacent side is \(\frac{5}{13}\).