Answer
All real numbers except $-5$ and $5$.
Work Step by Step
We know that $x^2-25=(x+5)(x-5).$
The denominator cannot be $0$, hence $x+5\ne0$ and $x-5\ne0$, therefore $x\ne-5$ and $x\ne5$.
Thus the domain is all real numbers except $-5$ and $5$.