A couple of points. I am thinking that there is quite a size difference between 5 weeks, and 14 weeks, the smaller birds will be on their home turf, but I think the older birds will be mean to the younger birds, maybe very mean.
I question the space you have for 7 chickens, none of those chickens are full grown yet, as in they will all get bigger and need more space. You basically have 36 square feet, I think you are going to have a lot of over crowding issues.
Without a doubt - it is not a bad idea to quarantine. However, if you can't do it right, you may as well not do it at all. To do it correctly, you need two totally separate coops/runs, they need to be a great distance apart, and you need to change clothes and footwear, and wash between sets of birds, and you need separate water and feed. Having the birds separated but within a few feet of each other is not a quarantine situation.
If you have a very valuable flock, with extensive breeding, or if you have a large flock, in both cases you are risking a financial loss, quarantine is of high importance. Unless you are so attached to your birds, that losing them will put you in a state of decline, the average small back yard flock, is really not a great risk, but it is a risk. More than once I have added birds, willy nilly and got a long just fine. However, in the spring, I have ordered some higher quality birds, and I will be quite a bit more careful what I add to that flock.
But I really think your biggest issue is the lack of space. With the space you have, I would think the 4 birds, once full grown will find it a bit small.
MrsK