Generally 4+ is recommended, but three COULD work, I suppose, as long as there's lots of ventilation and the food+water are in the run, not the coop. You may want to enclose the space under your coop to enlarge your run a bit.
10x4 is a bit small for 5 birds, but would work. Free ranging doesn't really count unless it's almost all day, almost every day. If you had a run that was big for more than 5 birds (for example, a 10x7 run for 6 birds) then you could probably add an extra.
You could try it, and they'd probably like it, but when building a coop that should be considered an extra, and your money should go to primarily necessities.