5. In a regular tetrahedron with edge length $5 \sqrt{6} \mathrm{~cm}$, there is a point $P$, which is at distances of $1 \mathrm{~cm}, 2 \mathrm{~cm}$, and $3 \mathrm{~cm}$ from three of its faces. Then the distance from $P$ to the fourth face is $\qquad$ $\mathrm{cm}$.
$5.4$