To factor the expression 5x^2 - 5y^2 - 10x + 10y, we can first factor out a common factor from the first two terms and the last two terms separately:

5x^2 - 5y^2 - 10x + 10y
= 5(x^2 - y^2) - 10(x - y)

Next, we can use the difference of squares formula to factor x^2 - y^2:

x^2 - y^2 = (x + y)(x - y)

Substitute this back into the expression:

5(x + y)(x - y) - 10(x - y)

Now, we can factor out a common factor of (x - y) from both terms:

= (x - y)(5(x + y) - 10)

Simplify the expression inside the parentheses:

= (x - y)(5x + 5y - 10)

Therefore, the factored form of 5x^2 - 5y^2 - 10x + 10y is (x - y)(5x + 5y - 10).