To solve the problem, we need to determine which of the given irrational numbers is greater than $-5$. Let's calculate each one step by step:

Options:

1. $-\sqrt{32}$

   • $\sqrt{32} \approx 5.656$
   • Thus, $-\sqrt{32} \approx -5.656$

2. $-\sqrt{22}$

   • $\sqrt{22} \approx 4.690$
   • Thus, $-\sqrt{22} \approx -4.690$

3. $-\sqrt{11}$

   • $\sqrt{11} \approx 3.317$
   • Thus, $-\sqrt{11} \approx -3.317$

4. $-\sqrt{41}$

   • $\sqrt{41} \approx 6.403$
   • Thus, $-\sqrt{41} \approx -6.403$

Comparing with $-5$:

• $-\sqrt{32} \approx -5.656$ (less than $-5$)
• $-\sqrt{22} \approx -4.690$ (greater than $-5$)
• $-\sqrt{11} \approx -3.317$ (greater than $-5$)
• $-\sqrt{41} \approx -6.403$ (less than $-5$)

Conclusion:

The numbers that are greater than $-5$ are:

• $-\sqrt{22}$ (Option B)
• $-\sqrt{11}$ (Option C)

Final Answer:

B and C

Would you like further clarification or a deeper explanation? Let me know!

Related Questions:

1. What is the general rule for comparing square roots of numbers?
2. How can you quickly estimate the square root of a number?
3. What are irrational numbers, and why are these examples considered irrational?
4. How do negative signs impact comparisons in problems involving square roots?
5. Can you think of real-world examples where comparing square roots is useful?

Tip:

When comparing square roots of numbers, it is helpful to know approximate values of perfect squares near them (e.g., $\sqrt{25} = 5$ and $\sqrt{36} = 6$) for faster estimations.