the reason youre not going to arrive at a contradiction usijg the parity of the two (even oddness) is because both n-3 and n-5 differ by 2, so they will have the same parity as each other and have opposite parity of n. if you know how to work with integers mod m, then I would work mod 7 and use some arithmetic to arrive a contradiction. if you haven't learned modular arithmetic, I would write the two numbers as a multiple of 7, then work with n and see how much more of a multiple of 7 it is.