To solve the expression $5 - \left[ \frac{96}{4} \times 3 - (16 - \frac{55}{5}) \right]$, let’s follow the order of operations (PEMDAS/BODMAS).

Step-by-Step Solution

1. Evaluate inside the brackets first:
   $5 - \left[ \frac{96}{4} \times 3 - (16 - \frac{55}{5}) \right]$

2. Division inside the brackets:
   $\frac{96}{4} = 24 \quad \text{and} \quad \frac{55}{5} = 11$

   Substitute these values back: $5 - \left[ 24 \times 3 - (16 - 11) \right]$

3. Perform the subtraction inside the inner parentheses:
   $16 - 11 = 5$

   Substitute this back: $5 - \left[ 24 \times 3 - 5 \right]$

4. Now, perform the multiplication:
   $24 \times 3 = 72$

   Substitute this back: $5 - \left[ 72 - 5 \right]$

5. Now, perform the subtraction inside the brackets:
   $72 - 5 = 67$

   Substitute this back: $5 - 67$

6. Finally, perform the subtraction:
   $5 - 67 = -62$

Final Answer:

None of the provided options (a, b, c, d) match the result $-62$. It seems there may be an issue with the options given.

Would you like further details or have any questions?

---

Here are 5 related questions to explore further:

1. What would the answer be if the inner expression was altered slightly, like using addition instead of subtraction?
2. How would changing the order of operations impact the final answer?
3. If we replaced the division symbol with multiplication, how would the calculation proceed?
4. What if the expression had additional parentheses? How would that affect the calculation?
5. Why is following the order of operations critical in complex expressions?

Tip: Always double-check each step when dealing with nested operations to avoid small mistakes.