1. **Problem:** List the elements of the set $\{ x : x \in \mathbb{N}, 5 < x < 12 \}$ where $\mathbb{N} = \{1, 2, 3, \ldots\}$. 2. **Understanding the problem:** We want all natural numbers greater than 5 and less than 12. 3. **Solution:** The natural numbers between 5 and 12 are $6, 7, 8, 9, 10, 11$. 4. **Final answer:** $$\{6, 7, 8, 9, 10, 11\}$$