Answer
$(-\infty,-5]U[-2,2]$.
Work Step by Step
Step 1. Factor the inequality as $x^2(x+5)-4(x+5)\le0$ or $(x+5)(x+2)(x-2)\le0$.
Step 2. Identify the boundary points $x=-5,-2,2$ and intervals $(-\infty,-5],[-5,-2],[-2,2],[2,\infty)$.
Step 3. Choose test values for each interval $x=-6,-3,0,3$ and test the inequality to get $True,\ False,\ True,\ False$.
Step 4. We can identify the solution intervals $(-\infty,-5]U[-2,2]$.
