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]).