1. **State the problem:** We are given two inequalities: $x < -5$ and $x \geq -2$. We want to understand the solution set for these combined conditions. 2. **Analyze each inequality:** - $x < -5$ means all values of $x$ less than $-5$. - $x \geq -2$ means all values of $x$ greater than or equal to $-2$. 3. **Combine the inequalities:** The problem states $x < -5$ and $x \geq -2$ simultaneously. For a number to satisfy both, it must be less than $-5$ and at the same time greater than or equal to $-2$. 4. **Check for overlap:** The set of numbers less than $-5$ is $(-\infty, -5)$. The set of numbers greater than or equal to $-2$ is $[-2, \infty)$. 5. **Conclusion:** These two sets do not overlap because $-5 < -2$. There is no number that is both less than $-5$ and greater than or equal to $-2$. **Final answer:** The solution set is the empty set, meaning no values of $x$ satisfy both inequalities simultaneously.