jmc

First we use the property that $a\equiv b(\mathrm{mod}m)$ implies $a^c\equiv b^c(\mathrm{mod}m)$.

Since $225\equiv 4(\mathrm{mod}17)$ and $327\equiv 4(\mathrm{mod}17)$, $$225^{66}-327^{66}\equiv 4^{66}-4^{66}=\boxed{0}(\mathrm{mod}17).$$