Recursion Help (I don't get this)

Question

I feel so stupid. I just can't understand recursion.
     public static int fib(int n)
          int result;
          if (n <=2)
               result = 1;
          else
               result = fib(n-1) + fib(n-2);
          return result;
     }The above is the famous Fibonacci method. But I DON'T GET IT. How the heck does this work? I don't understand how the recursive case works (result = fib(n-1) + fib(n-2)).
The way I understand it:
If we were to call call fib(5)...
recursive case:
result = fib(n-1) + fib(n-2); -> 4 + 3
The result would be 7, and then we would be done because we've reached the base case (n <=2). The correct answer is 5, so I'm obviously wrong. I just can't grasp this key concept. I'm feeling very noobish. :(

Answer 1

I should add that recursion is related to
mathematical induction, a powerful tool in
mathematics.
And once you get used to thinking about recursion,
you should see that in many ways recursive solutions
are simpler and clearer than non-recursive approaches.Ever so true but an efficient recursive solution should use a stack of
depth log(n), where n is the problem size, at most. It should also not
recompute what has been computed before.
The naive recursive fibonacci function doesn't fit that bill: it uses a stack
of size n for the calculation of fib(n) and it recalculates what has been
calculated before many times.
kind regards,
Jos