How can I get the back piece of the Ipad (5th Generation)

I guess what's left on the back of your housing is some kind of adhesive that might be removed one way or the other. Some adhesives are water based, others solvent based..depending on the solvent it might be melted by alcohol, isopropyl alcohol, turpentine or the likes. You might be better off trying various solvents until you cross the right one, less expensive and time consuming, replacing the housing takes hours let alone the risk of damaging something in the process. A mild heat could help in the task.