If it is not a space issue now, it soon will be. Personally, I think it is a space issue and that none of your birds can really get away from each other. There is no space to fly in that set up, no place to jump up or to roost in that area. There is no where for the birds to scratch and dig. Are they on a wire floor? In my own set up, my 4-5 week old chicks are roosting several feet off the ground by that age.
5 birds will shortly need a coup that equals at least 20 square feet, so think 4 feet by 5 feet, which I think is about the size of what you have now. The attached run should be about 50 square feet or about 5 feet x 10 feet. So all together you need a minimum of 14 x 5 feet.
Personally in the run, I have a pallet up on blocks that birds can get under, or on top. I have a pallet leaned up against the wall, where a bird can get into the shade, or just out of sight of it's tormentors.
Birds establish pecking orders by pecking another bird, until the lower bird flees. Your lowest bird has no where to go to indicate that it is accepting the lowest position, so they keep pecking. Boredom may be part of it, but the biggest part is lack of space and lack of hideouts.
Coups and runs, (my opinion) should be tall enough to stand up in, it makes them easier to clean, and it gives considerable more space to your birds, as space is truly a 3 dimensional space.
That set up, might work for a brooder, but your birds are outgrowing it. If that is your long term coop, you are going to need to severely cull your flock, or the problems are going to get much worse.
Hope you have another coop.
Mrs K