Answer
$\left[ 4,5 \right]$
Work Step by Step
Using the properties of inequality, the solution to the given inequality, $
5\le2x-3\le7
,$ is
\begin{array}{l}\require{cancel}
5+3\le2x-3+3\le7+3
\\\\
8\le2x\le10
\\\\
\dfrac{8}{2}\le\dfrac{2x}{2}\le\dfrac{10}{2}
\\\\
4\le x\le5
.\end{array}
Hence, the solution is the interval $
\left[ 4,5 \right]
.$