1. The problem asks us to find between which two integers the number $\sqrt{23}$ lies. 2. Recall that $\sqrt{n}$ is the positive number which when squared equals $n$. 3. We need to find integers $a$ and $b$ such that $a < \sqrt{23} < b$. 4. Check perfect squares near 23: - $4^2 = 16$ - $5^2 = 25$ 5. Since $16 < 23 < 25$, it follows that $4 < \sqrt{23} < 5$. 6. Therefore, $\sqrt{23}$ is between the integers 4 and 5. Final answer: $\boxed{4 \text{ and } 5}$