We know that $\frac{n}{0}$ is undefined for all $n \in \mathbb{R}$ and $\sqrt{x}$ is only defined for $x \geq 0$. The first condition applies to the first term in the denominator and both conditions apply to the second, giving us

$$

(1-x) \neq 0 \text { and } 5-x^{2}>0

$$

The first condition implies $x \neq 1$ while the second implies $|x|<\sqrt{5}$. Putting these together, we find that the domain is

$$

\{x|x \neq 1,| x \mid<\sqrt{5}\} \text { or }(-\sqrt{5}, 1) \cup(1, \sqrt{5})

$$