Answer
$(-\infty, -3) \cup (2, +\infty)$
Work Step by Step
RECALL:
$\\\\|a|\gt; b \longrightarrow a \gt b \text{ or } a \lt -b$
$\\\\$Use this definition of absolute value to have:
$\\\\|2x+1| \gt 5 \color{red}\longrightarrow \color{black}2x+1 \gt 5 \text{ or } 2x+1 \lt -5$
$\\\\\\$Solve each inequality to have:
$\\\\2x \gt 5-1 \text{ or } 2x \lt -5-1
\\\\2x \gt 4 \text{ or } 2x \lt -6
\\\\x \gt 2 \text{ or } x \lt -3$
$\\\\\\$Thus, the solution to the given inequality is:
$\\\\(-\infty, -3) \cup (2, +\infty)$