Answer
$\dfrac{15\sqrt{2}+20}{2}$
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}{3\sqrt{2}-4}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{5}{3\sqrt{2}-4}\cdot\dfrac{3\sqrt{2}+4}{3\sqrt{2}+4}
\\\\=
\dfrac{15\sqrt{2}+20}{(3\sqrt{2})^2-(4)^2}
\\\\=
\dfrac{15\sqrt{2}+20}{9\cdot2-16}
\\\\=
\dfrac{15\sqrt{2}+20}{18-16}
\\\\=
\dfrac{15\sqrt{2}+20}{2}
.\end{array}
