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