Let's denote the length of the chord as 2x, and draw a perpendicular line from the center of the circle to the midpoint of the chord. This line will bisect the chord into two equal parts, each of length x. The perpendicular line is 5 cm long, as given in the problem statement. We can now use the Pythagorean theorem to find x:

x\(^2\) + 5\(^2\) = 13\(^2\)

x\(^2\) + 25 = 169

x\(^2\) = 144

x = 12

So, the length of each half of the chord is 12 cm, and the total length of the chord is 2x = 24 cm.

Therefore, the correct answer is 24cm.