Let's break down and simplify the given expression step by step.

The expression is:

$\frac{5}{3} \cdot \left(\frac{39}{5} \cdot \frac{5}{3} + \frac{25}{3} \cdot \frac{39}{5}\right) + \left(-\frac{30}{7} \cdot \frac{7}{11} + \frac{7}{11} \cdot \frac{16}{3}\right) \cdot 5 - \frac{17}{3} - \left(\frac{268}{15} - \frac{24}{7}\right) - \left(\frac{42}{15} - 4\right) - \frac{145}{\left(\frac{69 \cdot 36}{29}\right)} \div \frac{5}{23} + 25 \cdot 0.375 \cdot (-10) \cdot 1$

Let's solve it step by step:

1. Simplify the first term: $\frac{5}{3} \cdot \left(\frac{39}{5} \cdot \frac{5}{3} + \frac{25}{3} \cdot \frac{39}{5}\right)$

2. Simplify the second term: $\left(-\frac{30}{7} \cdot \frac{7}{11} + \frac{7}{11} \cdot \frac{16}{3}\right) \cdot 5$

3. Subtract the next term: $-\frac{17}{3}$

4. Subtract the complex fraction: $-\left(\frac{268}{15} - \frac{24}{7}\right)$

5. Subtract the next term: $-\left(\frac{42}{15} - 4\right)$

6. Simplify the division term: $-\frac{145}{\left(\frac{69 \cdot 36}{29}\right)} \div \frac{5}{23}$

7. Simplify the multiplication at the end: $25 \cdot 0.375 \cdot (-10) \cdot 1$

Finally, we sum all the results.

Let me compute this step by step.The simplified value of the given expression is approximately 12.89.

Would you like a detailed breakdown of how each part was computed or have any questions about the steps? Here are five related questions to consider:

1. How do you simplify complex fractions step by step?
2. What are some common mistakes to avoid when handling multiple operations in one expression?
3. Can you explain the process of multiplying and dividing fractions?
4. What strategies can be used to check if the answer is correct?
5. How does rounding affect the accuracy of your final answer?

Tip: When simplifying complex expressions, it’s helpful to work with fractions in their exact form as long as possible to avoid rounding errors.