Hello folks,

hope everyone is enjoying their weekend.

The problem I have is that my chain rubs a lot when I'm at the highest 2 gears and at the lowest 2 or 3 gears in the rear.

here is my drive train (it's composed of parts I've replaced as the previous ones have gone bad)

left and right shifters are shimano 105 5700 series, 10s and 3s.
front derailleur is 105 FD-5703
Front crank set is 105 5500 triple speed. 52-32-28 (I could be wrong about the 28) I'll check later and update accordingly.
Rear derailleur is Ultegra 6600 10s
rear casset is CS-6600 12-23
Chain is CN-6600.

Looking at the pdf for my FD-5703 I see that the minimum teeth difference is 11. I have a teeth difference of 10. My thought is to replace one of the cogs so i can be in that minimum of 11.

I found this one on ebay that looks promising FC-5603 but it states it's for 8/9 speed set up. That got me to wondering what is the difference between a 10 speed crankset and a 9 speed crank set? Is the derailer wider to keep the chain from rubbing at the highest and lowest gear?

using a smaller inner cog will allow me to drop the derailer closer to the outer cog where it's supposed to be. Right now it's really high because if I go down any lower the middle cog scrapes the derailer.