Hint: A little bit of algebra might help.

Answer: I have 14 apples and you have 28 apples.

We can easily work this out with a little algebra. I have A apples and you have B apples, then

  5 x (A - 7) = B + 7    [1]

        A + 7 = B - 7    [2]

From [1] we have:

      5A - 35 = B + 7
           5A = B + 42   [3]

From [2] we have:

       A + 14 = B        [4]

We can then use [4] in [3] to give:

           5A = (A + 14) + 42
           5A = A + 56
           4A = 56
            A = 14

Which gives B = 28 (by [4]).