Factor $50=5^{2}\times 2$. Rewrite the square root of the product $\sqrt{5^{2}\times 2}$ as the product of square roots $\sqrt{5^{2}}\sqrt{2}$. Take the square root of $5^{2}$.
$$5\times 5\sqrt{2}-8\sqrt{32}$$
Multiply $5$ and $5$ to get $25$.
$$25\sqrt{2}-8\sqrt{32}$$
Factor $32=4^{2}\times 2$. Rewrite the square root of the product $\sqrt{4^{2}\times 2}$ as the product of square roots $\sqrt{4^{2}}\sqrt{2}$. Take the square root of $4^{2}$.
$$25\sqrt{2}-8\times 4\sqrt{2}$$
Multiply $-8$ and $4$ to get $-32$.
$$25\sqrt{2}-32\sqrt{2}$$
Combine $25\sqrt{2}$ and $-32\sqrt{2}$ to get $-7\sqrt{2}$.
