5700 is second generation 10 speed. While not officially supported, you could probably get things to work by replacing the cassette and chain with 10 speed and keeping the current derailleurs and crank set. Next in line of ideal compatibility, I'd then change the chainrings, then the brake calipers (5700 is New Super SLR, tricolor I think is Super SLR), then I'd change the rear derailleur, then the front derailleur.
STI levers are the biggest single expense for a drivetrain, and 5700 works great, so if you already have the 5700 levers in hand I'd upgrade the rest of the drivetrain to match those rather than the other way around.