A rational function $f(x)$ is defined for all real numbers except for $x=-5$ and $x=7.$ We are given that $x=-5$ and $x=7$ are vertical asymptotes for $f(x).$ The first derivative of this function is given below:

$f^{\text{'}}(x)=\frac{x^2-1}{(x+5{)}^3(x-7{)}^3}$

List all local extreme points for $f(x).$