i use no.5 for everything from driven phesant, duck,rabbits, crows , pigeons the lot.
I tried no6 on pigeons before and found them ok but few got a full dose but carried on, they are surprisingly tough lil critters especially with a full crop, now i use nothing but 5s
You wont go wrong with 5s
some bloke was telling me that he uses 8s and 7.5s for pigeon, i cant see then taking them down at any worthwhile range.
edited to say i vouch for quality cartridges like express. i use Express super twenty fibre no5 does the trick....when i hit them.