To factor the expression 3x^2 - 6xy + 3y^2 - 5x + 5y, we can group the terms and factor by grouping.

First, let's group the terms:
(3x^2 - 6xy + 3y^2) - (5x - 5y)

Now, let's factor each group separately:
3x^2 - 6xy + 3y^2 can be factored as (x - y)(3x - 3y) or 3(x - y)(x - y)
- (5x - 5y) can be factored as -5(x - y)

Putting it all together, we have:
3(x - y)(x - y) - 5(x - y)

Notice that we have a common factor of (x - y). We can factor it out:
(x - y)(3(x - y) - 5)

Simplifying the expression inside the parentheses, we get:
(x - y)(3x - 3y - 5)

Therefore, the factored form of the expression 3x^2 - 6xy + 3y^2 - 5x + 5y is (x - y)(3x - 3y - 5).