I thought that the minimum number was for the safety of the chicks. That you had to have a certain minimum for body warmeth to better survival during transit. Does that sound right?
You're right, it doesn't explain the breed/sex minimum.
Nature's Hatchery has a minimum order of 2 chicks and they say you don't need to live near a major city (mypetchicken.com has a 3 chick minimum only if you live near a big city). Which means the original question is still there-- how can one place have a minimum order of 25 and another place have a minimum order of 2? The ease of filling orders does seem valid.
Lets look at the shipping costs of the two: 15-25 chicks avg $15.00, 3 chicks $35.00, as they add a heat pad etc. to keep the few warm. Now as to why 5 per breed? I say call the hatchery ask and post back