1. Read up on System cases. I believe you were trying to say that you want a mid-tower or full tower sized case.
2. What components will you be using in the rig?
There are a LOT of mid-tower cases that have 5 external 5.25" bays and a good amount of internal bays. The Coolermaster RC-531 has 5 external 5.25" bays and 4 internal 3.5" bays and it is only a mid-tower case. You need to be specific on what you will put in the system initially, desired expandability and price range.