I've hunted pheasants for 49 years. I went through a 7.5 phase for maybe one season. The theory being that you'd kill the bird with denser pattern, versus crippling (maybe the idea was you'd hit it in the head?)
Its all about the number of chances you have, that is bird population and how picky you are with shots. A few years back during an abundant crop of birds in ND where I now hunt, I shot nothing but a 410 and made myself only shoot birds that I had to kick up from in front of my pointing dog. But most of us can't be that picky most of the time. And we want to break wings and legs (can't hit the head on one going away when you can't even see the head.) 5's is what I shoot routinely, and would always recommend.
A crossing bird at 35 yards, 7.5s would be great... shoot it in the head! Not many crossing shots if hunting pheasants behind a dog. In Europe they used to (maybe still do) think shooting a pheasant up the arse (going away) was disgusting. Driven birds flying over you and toward you.... head shots can be done.