Answer
$x^{5}(x-1)(x^{2}+x+1)$
Work Step by Step
We can take out a common factor of $x^{5}$ from the expression:
$x^{8}-x^{5}=x^{5}(x^{3}-1)$
Then we realize that $x^{3}-1$ is the difference of two cubes so we can factor again:
$x^{5}(x^{3}-1)=x^{5}(x-1)(x^{2}+x+1)$
