# What is the domain and range for h(x)= x^2 - 5?

The domain is (probably) the whole of $\mathbb{R}$, the set of all real numbers since the function $h \left(x\right)$ is well defined for all values of $x \in \mathbb{R}$. The reason I say $\mathbb{R}$ rather than $\mathbb{C}$, $\mathbb{N}$, $\mathbb{Z}$ or $\mathbb{Q}$ is based on the notational convention that $x$ normally stands for a real number.
If the domain is $\mathbb{R}$, then the range is $\left\{y \in \mathbb{R} : y \ge - 5\right\}$.