If the domain of the function $f\left(x\right)=\frac{\sqrt{x^2-25}}{4-x^2}+{\log }_{10}(x^2+2x-15)$ is $(-\infty ,\alpha )\cup [\beta ,\infty )$  then  $\frac{{\alpha }^2+{\beta }^2}{2}=$_________________

 $x^2-25\ge 0\Rightarrow x\in (-\infty ,-5]\cup (5,\infty ]$
 $4-x^2\ne 0\Rightarrow x\ne \{-2,2\}$
 $x^2+2x-15>0\Rightarrow x\in (-\infty ,-5)\cup (3,\infty )$
$\therefore$ Domain  $x\in (-\infty ,-5)\cup [5,\infty )$
 $\alpha =-5,\beta =5$
$\frac{{\alpha }^2+{\beta }^2}{2}=25$