For (x + y) to be a factor of an expression, it means that when you divide that expression by (x + y), the remainder should be zero.

Let's test each of the options:

A. \(x^2 + y^2\)
If we divide \(x^2 + y^2\) by (x + y), the remainder is not zero. So, (x + y) is not a factor of \(x^2 + y^2\).

B. \(x^3 - y^3\)
If we divide \(x^3 - y^3\) by (x + y), we can use the difference of cubes formula:
\[x^3 - y^3 = (x - y)(x^2 + xy + y^2)\]

So, (x + y) is not a factor of \(x^3 - y^3\).

C. \(2x^2 - 3xy + y^2 - x + 1\)
If we divide \(2x^2 - 3xy + y^2 - x + 1\) by (x + y), the remainder is not zero. So, (x + y) is not a factor of \(2x^2 - 3xy + y^2 - x + 1\).

D. \(2x^3 + 2x^2y - xy + 3x - y^2 + 3y\)
If we divide \(2x^3 + 2x^2y - xy + 3x - y^2 + 3y\) by (x + y), the remainder is zero. Therefore, (x + y) is a factor of \(2x^3 + 2x^2y - xy + 3x - y^2 + 3y\).

E. \(x^5 - y^5\)
If we divide \(x^5 - y^5\) by (x + y), the remainder is not zero. So, (x + y) is not a factor of \(x^5 - y^5\).

Therefore, the correct answer is \(2x^3 + 2x^2y - xy + 3x - y^2 + 3y\).