To simplify the expression, we first need to distribute the negative sign in the second set of parentheses:

(3x^2 + xy - y^2) - (2x^2 + xy + 3y^2 - 5x^2 + y^2)

Now, remove the parentheses and combine like terms:

3x^2 + xy - y^2 - 2x^2 - xy - 3y^2 + 5x^2 - y^2

Combine like terms:

(3x^2 - 2x^2 + 5x^2) + (xy - xy) + (-y^2 - 3y^2 - y^2)
6x^2 + 0 + (-y^2 - 3y^2 - y^2)

Simplify the expression further:

6x^2 - 5y^2

Therefore, the simplified expression is 6x^2 - 5y^2.