Too small for that many birds, that is only 20 square feet, for 12 birds you need more like 48 square feet, and that's a minimum that is still too small in my opinion. It's always better to go bigger then the minimum requirements if at all possible. Happier birds = less stress and lessens the chances of a pecking problem getting started.
Either need a bigger coop or less birds.
At 5x4, you can house 4-5 hens if they also have at least a 7' x 7' dedicated outdoor run. My recommendation is the build a coop much bigger than you think you will need. I can tell you from experience, you will want more chickens! I started with a dozen hens, and now have two dozen chickens and a dozen ducks. I converted an old shed into my coop, and I wish I had more room! Crowding leads to behavior problems and increases the potential for disease.