To find the values of $x$ that are not in the domain of the function $g(x)$, we need to identify the values that make the denominator equal to zero. The function $g(x)$ is given by:

$g(x) = \frac{x + 5}{x^2 - 3x - 40}$

We need to find the roots of the denominator $x^2 - 3x - 40$. To do this, we solve the equation:

$x^2 - 3x - 40 = 0$

We can factor this quadratic equation:

$x^2 - 3x - 40 = (x - 8)(x + 5) = 0$

Setting each factor to zero gives the solutions:

$x - 8 = 0 \implies x = 8$ $x + 5 = 0 \implies x = -5$

Therefore, the values of $x$ that are not in the domain of $g$ are $x = 8$ and $x = -5$.

Hence, the answer is:

$x = 8, -5$

Would you like more details or have any questions?

Here are 5 more questions you might want to ask:

1. How do you find the domain of a rational function?
2. What are vertical asymptotes and how do you find them?
3. Can you explain the process of factoring quadratic equations?
4. How do you determine if a function has any holes in its graph?
5. What are the steps to simplify complex rational expressions?

Tip: When finding the domain of a function, always check for values that make the denominator zero, as these values will not be included in the domain.