5. For what value of $z$ does the function $h(z)=$ $=\sqrt{1.44+0.8(z+0.3)^{2}}$ take its minimum value?
Solution. The function $h(z)$ takes the smallest value if $z+0.3=0$, i.e., when $z=-0.3$. It is clear that at this value of $z$, points $E$ and $H$ coincide, i.e., points $E$ and $H$ coincide with point $Q$.

It is also clear that if $z=-0.3$, then the plane $K N_{1} M$ is perpendicular to the plane of the rectangle $N_{1} N M M_{1}$.