Answer
The other zeros are:
$x=\pm\sqrt2$.
Work Step by Step
The factor theorem says that if $f(c)=0$, then $(x-c)$ is a factor of $f(x)$ and if $(x-c)$ is a factor of $f(x)$, then $f(c)=0$.
We check $x=5$:
$f(5)=5^3-5(5)^2-2(5)+10=0$
thus, it is indeed a zero.
Then, we can write:
$f(x)=(x-5)(x^2-2)=(x-5)(x+\sqrt2)(x-\sqrt2)$.
where we used the fact that:
$(a+b)(a-b)=a^2-b^2$
Thus the other zeros are:
$x=\pm\sqrt2$.
