The set $N = \{ x \mid x \text{ is an integer and } -5 < x < -1 \}$ represents all integers that satisfy the condition that $x$ is greater than $-5$ and less than $-1$.

The integers between $-5$ and $-1$ (exclusive) are: $N = \{ -4, -3, -2 \}$

So, the set $N$ contains the integers $-4, -3,$ and $-2$.

Would you like more details or have any questions?

Related Questions:

1. How would the set change if the inequality was $-5 \leq x \leq -1$?
2. What would the set look like if it included all real numbers instead of just integers?
3. How can you represent this set on a number line?
4. What would the set look like if $x$ had to be a positive integer?
5. How can this set be expressed in interval notation?

Tip: When working with sets defined by inequalities, always check whether the boundaries are included (i.e., whether the inequality is strict or not).