Answer
$x^5(x-1)(x^2+x+1)$
Work Step by Step
We start by factoring out $x^5$:
$x^8-x^5=x^5(x^3-1)$
The polynomial $x^3-1$ is a difference of two cubes. That is, we have
$$
x^8-x^5=x^5(x^3-1)=x^5(x-1)(x^2+x+1)
.$$
We can not factor $x^2+x+1$ any further because it is a prime polynomial.
