Some systems of generators of the group $\operatorname{GL}(n,\mathbb Z)$ for $n\leqslant 5$

It is proved geometrically that the groups $\operatorname{GL}(n,\mathbb Z)$, $0<n\leqslant 5$, are generated by systems of generators of finite groups $G_n$ and, for each such $n$, one additional substitution $h(n)$.