The given function is $h(x) = \sqrt{x + 5}$. To find the domain of this function, we need to determine the values of $x$ that make the expression inside the square root non-negative because the square root function is only defined for non-negative numbers (i.e., the value inside the square root must be greater than or equal to zero).

Step-by-step process:

1. Set the expression inside the square root to be non-negative: $x + 5 \geq 0$
2. Solve for $x$: $x \geq -5$

Domain:

Thus, the domain of the function $h(x)$ is $x \geq -5$, or in interval notation: $\text{Domain of } h(x): [-5, \infty)$

Would you like more details, or do you have any questions about this process?

Here are 5 questions related to this concept:

1. What is the range of the function $h(x) = \sqrt{x + 5}$?
2. How does the graph of $h(x) = \sqrt{x + 5}$ look like compared to $f(x) = \sqrt{x}$?
3. What happens to the domain if the function was $h(x) = \sqrt{-x + 5}$?
4. How do you calculate the domain for a rational function?
5. What are the steps to find the domain when the function involves both square roots and fractions?

Tip: Always start by checking the inside of square roots or denominators when finding the domain of a function!