Factorize:

$x^{5}+x^{2}=x^{2}\left(x^{3}+1\right)$

$=x^{2}\left(x^{3}+1^{3}\right)$

$=x^{2}(x+1)\left(x^{2}-x \times 1+1^{2}\right)$

$=x^{2}(x+1)\left(x^{2}-x+1\right)$