Coop size

Not at all, the size of your coop is directly proportionate to your management style or how large you think it needs to be or want it to be to dual as a shed for feed and bedding. .

If you plan to have a run and ensure the chickens access in the run everyday then there is no need for that much space. I don't heat the coop so chickens have no need to be in there unless laying eggs or getting on roosts for the night. With that I only need a little more than 2 sqft per bird of floor space. Honestly, have a 4x4 coop that has had up to 9 chickens in over winter. That was too many I think but there were no problems with that. With 7 chickens it works perfectly fine, external mounted nesting box of course.

If you want nests inside the coop, not external mounted, and want a walk in coop to store metal cans of food in then yeah, you need a much larger coop. There are those that heat coops or simply lock birds in on cold days or if predators are spotted in the area keep locked in for days on end. With this management style you'll need 4 sqft or more of floor space per bird as it suddenly becomes their run for periods of time or all winter.

 

That depends. Are you going to free range? Are they going to have access to a large run? If they are going to be cooped up in the coop for long stretched in the winter I don't think thats big enough. Mines 4x8 with 3 hens and I can't imagine 7 in there for long periods of time. And mine have an automatic door that gives them outside access all the time. But if it's nasty out they'll hang out inside.

 

the run is a bit small but the house sounds like it is of good size

 

Much depends on your climate. If you have winters with snow and cold you need a bigger coop. If your weather is such that they are able to be out all the time, your size is good. Make your coop and run predator proof and you won't have to lock them in the coop, so your 5' x 5' will work.