This is a kind of dirty way to do it, but I would update all the ranks that = 15 to set = 16, then update all the ranks that =14 to set=15, ect. until you get to the point where you want to insert the rank (in your example: 5).
Same with deleting. in your example, set all ranks that = 8 to set = 7 (this is assuming that you have decided what to do with 7 ranks if any exists). Set the 9 to 8, ect.
You would have to repeat the command to insert
UPDATE Table1 SET Table1.rank = 16
WHERE (((Table1.rank)=15));
Decrementing the values of 16 and 15 until you reached the point that you want to insert.
There may be an easier way, I'm sure... but this should work in your case. (I would hate to do this for something that has 1000 rankings)