So the correct dimensions are 6 feet 5 inches by 3 feet 8 inches?
That makes 23.5 square feet.
For 5 chickens, that should be enough floor space.
I agree with your idea of making it taller.
Maybe you can take the top off, and expand it to the full height of the shed. That would make a fairly nice coop for 5 chickens, and you would be able to walk into it if you want to.
Running one roost the long way would cause trouble when they try to fly down and then run into the wall, but running two roosts across it the short way would probably work. I would probably put a roost 1 foot in from each end, which keeps them far enough apart that a chicken on one roost cannot peck a chicken on the other roost.
You could put two nestboxes on the walls, or even have the nestboxes stick out into the shed so you can easily collect eggs without walking into the coop.