The given function is:

$g(x) = \sqrt{5x + 25}$

To determine the domain of the function $g(x)$, we need to ensure that the expression under the square root is non-negative, because the square root of a negative number is not real (for real-valued functions).

So, we solve for:

$5x + 25 \geq 0$

Subtract 25 from both sides:

$5x \geq -25$

Now, divide by 5:

$x \geq -5$

Thus, the domain of $g(x)$ is all values of $x$ such that $x \geq -5$.

In interval notation, the domain is:

$[-5, \infty)$

Would you like more details or have any further questions?

Here are 5 related questions to explore:

1. How do you find the domain of a function with multiple terms inside the square root?
2. What happens if the inequality results in no real solutions?
3. How do you express the domain for a logarithmic function?
4. Can you explain how to graph the domain of this function on a number line?
5. How do transformations (shifting or stretching) affect the domain of square root functions?

Tip: Always remember, the domain of a square root function requires the expression inside the square root to be greater than or equal to zero.