What is 5 + 10 5 5 - 2 20 - 32 + 50 equal to ?

Answer: Option D

$$\begin{array}{rl}& \text{Given,}\\ & \frac{5+\sqrt{10}}{5\sqrt{5}-2\sqrt{20}-\sqrt{32}+\sqrt{50}}\\ & =\frac{5+\sqrt{10}}{5\sqrt{5}-2\times 2\sqrt{5}-2\times 2\sqrt{2}+5\sqrt{2}}\\ & =\frac{5+\sqrt{10}}{5\sqrt{5}-4\sqrt{5}-4\sqrt{2}+5\sqrt{2}}\\ & =\frac{5+\sqrt{10}}{\sqrt{5}+\sqrt{2}}\\ & =\frac{\sqrt{5}\left(\sqrt{5}+\sqrt{2}\right)}{\sqrt{5}+\sqrt{2}}\\ & =\sqrt{5}\end{array}$$