5. As shown in Figure $1, A B C D-A_{1} B_{1} C_{1} D_{1}$ is a cube with an edge length of 100 cm,

Point $P$ starts from vertex $A$
and moves at a speed of 3 cm/s
along the line segment $A C_{1}$ uniformly.
Point $Q$ starts from vertex
$A_{1}$ at the same time as point $P$,
moving at a speed of 2 cm/s
along the line segment $A_{1} B_{1}$ uniformly. During the movement, the shortest distance of $P Q$ is $\qquad$ (accurate to 0.0001 cm).
5.71.1275 cm