Answer
$[-2,5]$.
Work Step by Step
Step 1. $x^2-3x-10\le0 \longrightarrow (x+2)(x-5)\le0$.
Step 2. Identify boundary points $x=-2,5$ and form intervals $(-\infty,-2],[-2,5],[5,\infty)$.
Step 3. Choose test values $x=-3,0,6$ to test the inequality and get results $False,\ True,\ False$.
Step 4. Thus we have the solution $[-2,5]$.