The chord being 5 cm away from the center tells us it's perpendicular to the diameter of the circle. Here's how to find the length of the chord:

Draw a diagram: Imagine a circle with center O, radius 13 cm, and a chord AB perpendicular to the diameter passing through O. Draw another line segment OL from O perpendicular to the chord AB.

Identify key points:

O is the center of the circle.
The radius (OA) is 13 cm.
Point L is the midpoint of chord AB because the perpendicular drawn from the center of a circle to a chord bisects the chord.
OL is the distance from the center to the chord (given as 5 cm).
Use the Pythagorean Theorem: We have a right triangle OLA with a right angle at L. We know the length of the leg OL (5 cm) and the hypotenuse OA (13 cm). We want to find the length of leg AL (half the length of the chord AB).

Apply the Pythagorean theorem:

OA^2 = OL^2 + AL^2
Solve for AL:

Substitute the known values: 13^2 = 5^2 + AL^2
Simplify and solve for AL: 169 = 25 + AL^2 ; AL^2 = 144 ; AL = √144 = 12 cm
Find the length of the chord (AB):

Since we know the perpendicular from the center bisects the chord, the total length of the chord is twice the length AL: AB = 2 * AL = 2 * 12 cm = 24 cm
Therefore, the length of the chord located 5 cm away from the center of the circle is 24 cm.