The given expression simplifies to:

$\frac{8 \cdot \log(2)^2}{3 \cdot \log(3)^2} + \frac{3 \cdot \log(5)^2}{5 \cdot \log(2)^2}$

This expression involves logarithmic terms and their squares. Let me know if you'd like to proceed further with numerical approximations or more details on the simplification.

Would you like any specific clarifications or further steps?

Here are 5 related questions for deeper understanding:

1. How do logarithmic properties affect simplifications in similar problems?
2. Can you express the result with a common denominator?
3. How would the expression change if different logarithmic bases were used?
4. What would happen if the logarithmic terms were expanded or factored?
5. How would this result apply in practical contexts like signal processing?

Tip: When dealing with logarithms, try using properties such as the product rule, quotient rule, and power rule to simplify complex expressions.