#### Answer

$\left( -\dfrac{7}{3},-1 \right)$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To solve the given inequality, $
-8\gt3x-5\gt-12
,$ use the properties of inequality to isolate the variable.
$\bf{\text{Solution Details:}}$
Using the properties of inequality, the inequality above is equivalent to
\begin{array}{l}\require{cancel}
-8+5\gt3x-5+5\gt-12+5
\\\\
-3\gt3x\gt-7
\\\\
\dfrac{-3}{3}\gt\dfrac{3x}{3}\gt-\dfrac{7}{3}
\\\\
-1\gt x\gt-\dfrac{7}{3}
\\\\
-\dfrac{7}{3}\lt x\lt -1
.\end{array}
Hence, the solution set is the interval $
\left( -\dfrac{7}{3},-1 \right)
.$