Answer
$3\sqrt{7}-9\sqrt{2}$
Work Step by Step
$\displaystyle \frac{5}{\sqrt{2}+\sqrt{7}}\color{red}{ \cdot\frac{ \sqrt{2}-\sqrt{7}}{\sqrt{2}-\sqrt{7}} }=\frac{5(\sqrt{2}-\sqrt{7})}{(\sqrt{2})^{2}-(\sqrt{7})^{2}}=$
$=\displaystyle \frac{5(\sqrt{2}-\sqrt{7})}{2-7}==\frac{5(\sqrt{2}-\sqrt{7})}{-5}=-(\sqrt{2}-\sqrt{7})=-\sqrt{2}+\sqrt{7}$
$2\sqrt{32}=2\sqrt{16\cdot 2}=2\sqrt{16}\cdot\sqrt{2}=2\cdot 4\sqrt{2}=8\sqrt{2}$
$\sqrt{28}=\sqrt{4\cdot 7}=\sqrt{4}\cdot\sqrt{7}=2\sqrt{7}$
$problem=-\sqrt{2}+\sqrt{7}-8\sqrt{2}+2\sqrt{7}$
... add like terms
$=3\sqrt{7}-9\sqrt{2}$
