The result of the given expression $4^5 + \left( \frac{7^3 \times 5!}{2^3 - 2!} \right)$ is 7884.

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Here are some related questions for further exploration:

1. How are factorials used in complex expressions?
2. What is the significance of exponentiation in mathematical calculations?
3. How does order of operations (PEMDAS/BODMAS) influence the outcome of expressions like this?
4. What are common mistakes to avoid when simplifying factorial-based expressions?
5. How could this expression be extended to include trigonometric functions?

Tip: When working with factorials and exponents together, always evaluate factorials first for clarity!