Answer
$ (5,\infty)$.
Work Step by Step
Step 1. For $(x-5)(x+2)^2\gt0$, identify boundary points as $x=-2,5$.
Step 2. Form intervals $(-\infty,-2),(-2,5),(5,\infty)$.
Step 3. Choose test values for each interval $x=-3,0,6$.
Step 4. Test the inequality to get results: $False,\ False,\ True$
Step 5. We have the solution $ (5,\infty)$.
