The given set $I = \{ y \mid y \text{ is an integer and } -5 < y - 3 \}$ can be rewritten by solving the inequality for $y$.

Starting with the inequality: $-5 < y - 3$ Add 3 to both sides: $-5 + 3 < y \quad \Rightarrow \quad -2 < y$

This means $y$ must be an integer greater than $-2$. Therefore, the set $I$ includes all integers greater than $-2$, which can be written as: $I = \{ -1, 0, 1, 2, 3, 4, \dots \}$

This is the set of all integers starting from $-1$ and increasing without bound.

Would you like any further details or clarification?

---

Here are five related questions:

1. How do you solve inequalities involving absolute values?
2. How would the set change if $y - 3 \leq -5$?
3. What happens if you add a condition like $y < 10$?
4. Can you list the elements of the set $\{ y \mid -2 \leq y \leq 5 \}$?
5. How do you represent an infinite set on a number line?

Tip: When solving inequalities, always remember to reverse the inequality sign if you multiply or divide by a negative number!