Chapter 10 - Exponents and Radicals - 10.5 Expressions Containing Several Radical Terms - 10.5 Exercise Set - Page 661: 62

$\dfrac{20+5\sqrt{5}}{11}$

Multiplying by the conjugate of the denominator, the rationalized-denominator form of the given expression, $ \dfrac{5}{4-\sqrt{5}} ,$ is \begin{array}{l}\require{cancel} \dfrac{5}{4-\sqrt{5}}\cdot\dfrac{4+\sqrt{5}}{4+\sqrt{5}} \\\\= \dfrac{5(4)+5(\sqrt{5})}{4^2-(\sqrt{5})^2} \\\\= \dfrac{20+5\sqrt{5}}{16-5} \\\\= \dfrac{20+5\sqrt{5}}{11} .\end{array}