Answer
See explanations.
Work Step by Step
Step 1. To rationalize a denominator, we need to multiply both the numerator and the denominator with the conjugate of the denominator which is an expression containing radicals.
Step 2. In the case of $\frac{1}{\sqrt 5}$, multiply $\frac{\sqrt 5}{\sqrt 5}$ to get $\frac{1}{\sqrt 5}=\frac{1}{\sqrt 5}\times\frac{\sqrt 5}{\sqrt 5}=\frac{\sqrt 5}{5}$
Step 3. In the case of $\frac{1}{5+\sqrt 5}$, multiply $\frac{5-\sqrt 5}{5-\sqrt 5}$ to get $\frac{1}{5+\sqrt 5}=\frac{1}{5+\sqrt 5}\times\frac{5-\sqrt 5}{5-\sqrt 5}=\frac{5-\sqrt 5}{25-5}=\frac{5-\sqrt 5}{20}$
