That is the definition of a derivative.
All you have to do is plug x+h into wherever there is an x
so you will get (x+h)3-5(x+h)+1 - (x3 -5x +1) all divided by h with the lim as h approaches 0
You wil then expand out
x3 + 3x2h + 3xh2+h3-5x-5h+1 -x3+5x-1
x3 and -x3 cancel each other out +1 and -1 cancel each other out -5x and +5x cancel each other out so you will get an equation with "h"'s in it.
That is the top. Now we will put this back into the limit equation
You can factor out one h from the top to get h that will cancel out with the h from the bottom to get
3x2 + 3xh +h2-5
You set the limit as h approaches 0 of this
and plug in 0 wherever there is an h to get
3x2 + 3x(0) + (0)2-5
Your derivative to this is 3x2-5
It's not so easy to type this out, but I hope it helps!!