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]). QED.