Factor $175=5^{2}\times 7$. Rewrite the square root of the product $\sqrt{5^{2}\times 7}$ as the product of square roots $\sqrt{5^{2}}\sqrt{7}$. Take the square root of $5^{2}$.
$$7-\frac{3}{5}\times 5\sqrt{7}+2\sqrt{7}$$
Cancel out $5$ and $5$.
$$7-3\sqrt{7}+2\sqrt{7}$$
Combine $-3\sqrt{7}$ and $2\sqrt{7}$ to get $-\sqrt{7}$.
