It looks like you've uploaded an image with a mathematical expression that needs simplification. The expression is:

$\frac{(a-5)^4 - (b+5)^4}{(a-5)^3 - (b+5)^3}$

This is a difference of powers problem. To simplify it, we can factor the numerator and the denominator.

We can apply the identity for the difference of cubes and the difference of squares as follows:

• Difference of cubes: $x^3 - y^3 = (x - y)(x^2 + xy + y^2)$

• Difference of squares: $x^4 - y^4 = (x^2 - y^2)(x^2 + y^2)$

Using these identities will allow us to factor the expression and simplify it further. Let me know if you'd like to go through the detailed steps or if you have any other questions.

Would you like me to break down the steps for this? Or is there a specific part you'd like me to focus on?

Here are 5 related questions that may help expand the knowledge:

1. How do you factor the difference of cubes?
2. What are some useful identities for simplifying algebraic expressions?
3. How do you simplify complex algebraic fractions?
4. What is the general formula for factoring the difference of squares?
5. How can you approach higher-degree polynomials in a similar way?

Tip: Always check for common algebraic identities like difference of squares, cubes, and factoring out terms when simplifying algebraic expressions.