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