Answer
$f(x)=x^{3}$ and $a=5$
Work Step by Step
The derivative at a point $a$ is defined as
$f'(a)=\lim\limits_{x \to a}\frac{f(x)-f(a)}{x-a}$
But, given that
$f'(a)=\lim\limits_{x \to 5}\frac{x^{3}-125}{x-5}\,\,\,\,$
Comparing right-hand sides of both the equations above, we obtain
$a=5$ and $f(x)=x^{3}$
