Generally I shoot either 3 or 5. I prefer 5 but some barrels heat up faster than others, some guns kick more than others, and so on. Sorta depends on how much time and abuse I want to put in.
I generally time my shots at a fixed interval which I tailor to each gun depending on how fast it seems to heat up. Some guns don't really heat up for the first 20-25 shots so I'm inclined to shoot 5 shot groups with those. Others, like a 7mm STW I had, run up to 7-8 minutes between shots, so I lean towards 3 shot groups so I don't die of old age sitting at the shooting bench. (One afternoon I had the range to myself and I fell asleep between shots. Oops.)
The key thing, which probably explains not caring much about 3 shot vs 5 shot groups, is I'm not trying to find a load I guarantee works during initial development, what I'm mostly doing is eliminating loads. A single half inch 200 yard group probably isn't enough to count a load as a winner, but unless I yank the shot, a 6" 200 yard group is a pretty good sign that one is not worth pursuing.
What I really look for is a region of powder charges for a given powder and bullet that give about the same accuracy and group center location. That suggests not only accuracy but a certain stability of accuracy. I don't want something that's real good but goes all to h*ll, either by groups opening up badly or change impact point, if I'm off by a couple tenths of a grain. I want something that's stable plus or minus a grain or more if possible.
Before I put the stamp of approval on a load, it has to pass muster not only at 100 or 200 yards where I'm doing load development, but out at whatever max distance I've decided I might use it at.