Just draw a circle with center C.
then draw a chord. AB.
draw a radius to one end of this chord CA.
draw a perpendicular line from the center to the chord at point P (CP).
Now you have a right triangle CAP.
as per pythagoras theorem,
CA ^2 = AP^2 + PC^2.
PC = 5 as per question.
13^2 = 5^2 + AP^2.
gives AP = 12.
therefore AB = 2 AP as perpendicular to chord from center is bisector of chord.
AB = 2 * 12 = 24.
As I became crazy, I drew an illustration of this.
