1. **State the problem:** Solve the inequality $|5 - x| \geq -6$. 2. **Recall the property of absolute values:** The absolute value of any real number is always non-negative, meaning $|a| \geq 0$ for any $a$. 3. **Analyze the inequality:** Since $|5 - x|$ is always $\geq 0$, it will always be greater than or equal to $-6$ because $-6$ is negative. 4. **Conclusion:** The inequality $|5 - x| \geq -6$ holds true for all real numbers $x$. 5. **Final answer:** The solution set is $\boxed{(-\infty, \infty)}$. This means every real number satisfies the inequality.