#### Answer

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

#### Work Step by Step

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}