On (2,3)-generation of matrix groups over the ring of integers

The groups $\mathrm{GL}(5,\mathbb{Z})$, $\mathrm{SL}(5,\mathbb{Z})$, $\mathrm{SL}(6,\mathbb{Z})$, $\mathrm{GL}(7,\mathbb{Z})$ and $\mathrm{SL}(7,\mathbb{Z})$ are (2,3)-generated.