Answer
$(x+5)(x^{2}-2)$
Work Step by Step
$ x^{3}+5x^{2}-2x-10=\quad $
Factor in pairs; factor out $ x^{2}$ from the first pair, and $-2$ from the second
$=x^{2}(x+5)-2(x+5)$
$=(x+5)(x^{2}-2)$
We could treat the second parentheses as a difference of squares, using $(\sqrt{2})^{2}=2$, but factoring implies integer coefficients, so we stop here.
