Answer
$(-\infty,-5)\cup(-2,\frac{1}{2})$.
Work Step by Step
Step 1. For $(2x-1)(x+2)(x+5)\lt0$, identify boundary points as $x=-5,-2,\frac{1}{2}$.
Step 2. Form intervals $(-\infty,-5),(-5,-2),(-2,\frac{1}{2}),(\frac{1}{2},\infty)$.
Step 3. Choose test values for each interval $x=-6,-3,0,1$.
Step 4. Test the inequality to get results: $True,\ False,\ True,\ False$
Step 5. We have the solution $(-\infty,-5)\cup(-2,\frac{1}{2})$.
