No question bigger shot is more effective but you need to factor in pattern density too, in other words if I could throw as many 5's in a load as I can 7's then I too would opt for the former. Unfortunately to get 350 number 5's you'd prolly have to buy 48g loads.
The reason I even tried 32/36 gram loads of 5 shot was because I kept reading about these incredible distance birds people were pulling off when they wouldn't quite commit to decoys or when chasing the ones that flared off after a shot was fired. What I actually found was that they were no better at ordinary range and if you did push them out a bit the lack of pattern density meant fewer shot actually connected with the birds, I kept having to walk 200 yards to fetch birds that "towered" - no thanks, what's the point of that ? You can knock down birds at respectable distance with 7's and 3/4 choke.
those 7's will pole ax a 35 yard pigeon through 1/2 choke, I even find them excellent for very high flighting birds. 
