#### Answer

y=$\sqrt {41}$$\approx$6.4

#### Work Step by Step

Let x represent the distance from the chord to the center of the circle with a radius of 13 inches. Let y represent the radius of the other circle.
x$^2$=13$^2$-5$^2$
x$^2$=169-25
x$^2$=144
x=12
16-12=4
y$^2$=4$^2$+5$^2$
y$^2$=16+25
y$^2$=41
y=$\sqrt 41$$\approx$6.4