The set of points from $-5$ to $-1$ but excluding $-2$ and $-1$ can be written as the following union of intervals:

$[-5, -2) \cup (-2, -1)$

This represents the interval from $-5$ to $-2$ (excluding $-2$), and the interval from just after $-2$ to $-1$ (excluding $-1$).

Would you like any more details or have any questions?

Here are 5 related questions to explore further:

1. How do you represent the union of intervals graphically on a number line?
2. What is the difference between open and closed intervals?
3. How would the interval notation change if $-2$ were included?
4. What is the difference between union and intersection of intervals?
5. How can set-builder notation be used to represent the same set?

Tip: When working with intervals, remember that square brackets $[ \, ]$ indicate that the endpoints are included (closed interval), while parentheses $( \, )$ indicate that the endpoints are not included (open interval).