I once acquired a brand new full carb set that had been taken from a customer's bike. His bike refused to idle on #5 cylinder and the dealership tried to tune out the problem but failed. They fitted a new set of carbs and the problem was solved. What I found was that the mixture being delivered to #5 cylinder was over rich--beyond any relativity to a stoichiometric air/fuel ratio. I found that there was a restriction in the air-idle circuit on that carb, and eventually found where it was by drilling out some of the small blanking plugs in the carb body. Under the diaphragms there is a small blanking plug on side of the carb. I carefully removed the plugs with a two mm drill and a fine self tapping screw. In the gallery thus exposed I saw a small brass air jet in each. One of them (the one on #5 cylinder) looked to have some sort of corrosion on it. I have some very small jet drills and carefully cleaned the dirty jet with a drill and compressed air. Made some new plugs and fitted them and from then on the carbs worked as intended.