#### Answer

The distance between the chords is 1.

#### Work Step by Step

Let x represent the distance between chord AB and point P. Let y represent the distance between chord CD and point P.
x$^2$=5$^2$-4$^2$
x$^2$=9
x=3
y$^2$=5$^2$-3$^2$
y$^2$=16
y=4
y-x=4-3=1