Question 832224
You can graph it to check how many real roots it has.
.
.
{{{ graph( 300, 300, -5, 5, -5, 5, x^5-5x^3+10x-1) }}} 
.
.
It has one real root which is not an integer root so numerical methods would be the best way to find the real root.
Using Newton's method, in one iteration, I found the root {{{x=0.100507}}}.
Methods to find complex roots are much more complicated.