First have you patterned your shotgun aiming it at a very large sheet of poster paper? The reason I ask is that many, many, shotguns do not throw the center of their patterns to the exact point of aim ofthe front sight. In fact I have seen some that shot as much as 6 or 7 inchs off at 30 yards. Easily enough to make you miss a turkeys head. The addition of an adjustable sight can correct the problem if it exists. Also a set of front and rear fiber optic sights will make you keep your head down when aiming. Liftingof the headbeing a common reason for missing as well.
I did a little research on the internet yesterday and it seems that some guys say #6 shot doesnt have much knock down power at slightly longer shots. Maybe I should switch to #5?
Lead 6's will typically be fine out to 40 yards if your gun patterns them well but that is the maximum range I'd go with them. Lead 5's will certainlystay lethal a little farther but you need to see how far they hold together in a dense enough pattern. (Did I mention patterning your gun yet?) (Do I sound like an irritating stuck record on that point? LOL!) If so, it is only because that is the only way you can "know" what your gun is doing with a particular type of shot at a given distance. Outside some trigger time at the range all we can do is "guess" what the problem may be.