Answer
$$x ∈ (-\infty, -5] ∪ \{-3\} ∪ [2, +\infty)$$
Also see the image below.
Work Step by Step
$(x+3)^2(x-2)(x+5)\geq0$
Sketching the graph of equation $(x+3)^2(x-2)(x+5)$ gives us the Blue graph on the image above.
We need to locate the region, that is above $y=0$ ($x$-axis) line. So we have the solution:
$x ∈ (-\infty, -5] ∪ \{-3\} ∪ [2, +\infty)$
