The simplified expression is:

$\frac{(x - 5)(x + 5)}{8} \cdot \frac{(x - 1)}{(x + 5)(x + 5)} = \frac{(x - 5)(x - 1)}{8(x + 5)}$

Is there anything else you would like me to clarify or explain?

Here are 5 related questions that might interest you:

1. How can you quickly identify common factors in rational expressions?
2. What are the steps for simplifying complex fractions?
3. How does factoring help in simplifying division of rational expressions?
4. What techniques are best for dividing polynomials?
5. How can you check your simplified answer for accuracy?

Tip: Always cancel out the common factors across the numerator and denominator to fully simplify rational expressions.