Answer
$\left( -5,\dfrac{5}{2} \right)$
Work Step by Step
Using properties of equality, then,
\begin{array}{l}
0\lt\dfrac{5-2x}{3}\lt5\\\\
0\lt5-2x\lt15\\
-5\lt-2x\lt10\\
\dfrac{5}{2}\gt x\gt-5\\
-5\lt x\lt\dfrac{5}{2}
.\end{array}
In interval notation form, the solution is $
\left( -5,\dfrac{5}{2} \right)
$.