Normal sudoku rules apply.
Additionally, outside numbers show the total of the numbers moving into the grid in that direction before hitting the 5 - 5 is never included.
However, if this total would be 0 or 40, indicating the 5 is either on the near or far edge of the grid, the number is displayed as 20 instead.
(So for example: if a row was 1 2 3 9 5 6 7 8 4, the left side would indicate 15 (1+2+3+9) and the right side 25 (4+8+7+6))
A Microsoft Excel version of this puzzle can be downloaded here. This includes the solution.