To find the domain of the function $y = (x - 4)(x + 3)(x + 5)$, we need to identify any values of $x$ that would make the function undefined.

In this case, the function is a polynomial (a product of three linear factors), and polynomials are defined for all real numbers because there are no restrictions such as division by zero or square roots of negative numbers.

Therefore, the domain of the function is: $\boxed{(-\infty, \infty)}$

Would you like further details or have any questions?

Here are 5 related questions to explore further:

1. What is the range of the function $y = (x - 4)(x + 3)(x + 5)$?
2. What are the x-intercepts of the function?
3. How do you find the critical points of this polynomial function?
4. What is the behavior of the function as $x \to \infty$ and $x \to -\infty$?
5. How would you graph this function?

Tip: The domain of any polynomial is always all real numbers unless it's combined with other functions like fractions or square roots that may introduce restrictions.