Let's solve the given expression step by step. The expression is:

$5 - \left[ \frac{3}{8} \div \left\{ 2 \frac{1}{2} \times \left( 0.7 \text{ of } \left( \frac{1}{6} - \frac{1}{7} \right) \right) \right\} \right]$

Step 1: Simplify the expression inside the parentheses

We first simplify $\frac{1}{6} - \frac{1}{7}$.

$\frac{1}{6} - \frac{1}{7} = \frac{7 - 6}{42} = \frac{1}{42}$

Step 2: Multiply by 0.7 (as "0.7 of" means multiplication)

$0.7 \times \frac{1}{42} = \frac{0.7}{42} = \frac{7}{420} = \frac{1}{60}$

Step 3: Multiply by $2 \frac{1}{2}$ (convert to improper fraction)

Convert $2 \frac{1}{2}$ to an improper fraction: $2 \frac{1}{2} = \frac{5}{2}$

Now, multiply $\frac{5}{2} \times \frac{1}{60}$: $\frac{5}{2} \times \frac{1}{60} = \frac{5}{120} = \frac{1}{24}$

Step 4: Perform the division $\frac{3}{8} \div \frac{1}{24}$

Dividing fractions is equivalent to multiplying by the reciprocal: $\frac{3}{8} \div \frac{1}{24} = \frac{3}{8} \times \frac{24}{1} = \frac{3 \times 24}{8 \times 1} = \frac{72}{8} = 9$

Step 5: Subtract from 5

Now, subtract the result from 5: $5 - 9 = -4$

Final Answer:

$\boxed{-4}$

Would you like more details on any step or have any questions?

Here are five related questions:

1. How do you simplify expressions involving fractions?
2. What is the method to convert mixed numbers into improper fractions?
3. How do you multiply and divide fractions?
4. What is the importance of the order of operations in expressions?
5. How does multiplying a number by a fraction less than 1 affect its value?

Tip: When dealing with complex expressions, breaking them down into simpler parts and solving step-by-step is a highly effective strategy.