The given expression is:

$5x - 5y - ax + ay$

To factor this expression, we can group the terms and factor out common factors from each group.

Step 1: Group the terms: $(5x - 5y) - (ax - ay)$

Step 2: Factor out the common terms from each group: $5(x - y) - a(x - y)$

Step 3: Notice that $(x - y)$ is a common factor. So, factor it out: $(5 - a)(x - y)$

Thus, the factorized form is:

$(5 - a)(x - y)$

Would you like further explanation or details?

Here are 5 related questions to consider:

1. How do you factor more complex algebraic expressions?
2. What is the distributive property in algebra?
3. Can you explain how to factor expressions with three or more terms?
4. How does grouping terms help in factoring?
5. What strategies can be used when no common factor exists between terms?

Tip: Always look for common factors in groups of terms to simplify factoring.