Answer
The solution is $(-3,-1]$
Work Step by Step
$-1\lt2x+5\le3$
Subtract $5$ in all parts of the inequality:
$-1-5\lt2x+5-5\le3-5$
$-6\lt2x\le-2$
Divide by $2$ on all parts of the inequality:
$-\dfrac{6}{2}\lt\dfrac{2x}{2}\le-\dfrac{2}{2}$
$-3\lt x\le-1$
The solution is $(-3,-1]$