#### Answer

$-\dfrac{5\sqrt{6}}{12}$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To rationalize the given radical expression, $
\dfrac{-5}{\sqrt{24}}
,$ multiply both the numerator and the denominator by an expression that will make the denominator a perfect power of the index.
$\bf{\text{Solution Details:}}$
Expressing the radicand with a factor that is a perfect power of the index results to
\begin{array}{l}\require{cancel}
\dfrac{-5}{\sqrt{4\cdot6}}
\\\\
\dfrac{-5}{\sqrt{(2)^2\cdot6}}
.\end{array}
Multiplying both the numerator and the denominator by an expression that will make the denominator a perfect power of the index results to
\begin{array}{l}\require{cancel}
\dfrac{-5}{\sqrt{(2)^2\cdot6}}\cdot\dfrac{\sqrt{6}}{\sqrt{6}}
.\end{array}
Using the Product Rule of radicals which is given by $\sqrt[m]{x}\cdot\sqrt[m]{y}=\sqrt[m]{xy},$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
\dfrac{-5\sqrt{6}}{\sqrt{(2)^2\cdot6(6)}}
\\\\=
\dfrac{-5\sqrt{6}}{\sqrt{(2)^2\cdot(6)^2}}
\\\\=
\dfrac{-5\sqrt{6}}{2\cdot6}
\\\\=
\dfrac{-5\sqrt{6}}{12}
\\\\=
-\dfrac{5\sqrt{6}}{12}
.\end{array}