4x4 is real tight for 5 hens and a rooster. If you commit to never leaving them locked in there during their waking hours (they get up with the sun) when you have the flu or Saturday mornings after a late Friday night you might get away with it. When you do go on vacation, can you find someone that will be able to do that? Do you ever have weather when they can’t go outside? You are not giving yourself any flexibility with one that size.
Try laying out the inside. How would you set it up so they can roost without pooping in the food and water, if you plan on feed and water inside?
Why do you want the rooster? So you can hatch chicks? Where would they fit in that coop?
You have way too many nests. A general rule of thumb is one nest for every four hens with a flock your size. Two nests would be plenty.
You really want a run talk enough that you can walk in it without bumping your head.
How would you clean that coop out? You need to be able to access everywhere inside, maybe to fix something, to gather an egg if they don’t lay in a nest, to retrieve an injured chicken that may not want to be caught, something will come up.
It’s elevated which is not a bad idea. If you fence around the coop and include that in the run, that gives them a place other than in the coop to get out of the weather. Shade in the summer is really important. When you elevate it, you need to be able to access it under there so make it high enough you can see under there and retrieve an egg or injured chicken if you need to.
You’ll probably get feedback on the chicken wire. Occasionally you’ll see threads where a dog or raccoon tore chicken wire and killed the chickens inside. Chicken wire will keep chickens in, but it really won’t keep a determined big predator out. A lot of people will tell you that you have to use hardware cloth for a run, but I’m not one of those. It’s pretty expensive. I used 2” x 4” welded wire for my run. That keeps big predators out. I haven’t had this problem, but some people have had a raccoon reach through openings smaller than that and pull a chicken through in pieces to eat it. If you line the bottom inside of your run with chicken wire, just the bottom 18” or so, you can stop that. That combo will be a lot less expensive than hardware cloth.
That’s just a quick look. Hope you get some good out of this. Good luck!