Answer
$\dfrac{35-5\sqrt{3}}{46}$
Work Step by Step
Multiplying by the conjugate of the denominator and using $(a+b)(a-b)=a^2-b^2,$ the given expression, $
\dfrac{5}{\sqrt{3}+7}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{5}{\sqrt{3}+7}\cdot\dfrac{\sqrt{3}-7}{\sqrt{3}-7}
\\\\=
\dfrac{5\sqrt{3}-35}{(\sqrt{3})^2-(7)^2}
\\\\=
\dfrac{5\sqrt{3}-35}{3-49}
\\\\=
\dfrac{5\sqrt{3}-35}{-46}
\\\\=
\dfrac{35-5\sqrt{3}}{46}
.\end{array}
