Answer
$(-\infty,-2)$.
Work Step by Step
Step 1. For $(x-5)^2(x+2)\lt0$, 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: $True,\ False,\ False$
Step 5. We have the solution $(-\infty,-2)$.
