Factor $45=3^{2}\times 5$. Rewrite the square root of the product $\sqrt{3^{2}\times 5}$ as the product of square roots $\sqrt{3^{2}}\sqrt{5}$. Take the square root of $3^{2}$.
$$-\sqrt{5}+3+4\sqrt{3}-3\times 3\sqrt{5}$$
Multiply $-3$ and $3$ to get $-9$.
$$-\sqrt{5}+3+4\sqrt{3}-9\sqrt{5}$$
Combine $-\sqrt{5}$ and $-9\sqrt{5}$ to get $-10\sqrt{5}$.
