You need to do more research on this - I'm in the market for a new car that would take a 4 bike carrier in a hitch receiver. All of my research indicates that to safely carry 4 or more bikes, you'll need a Class 3 hitch, 2" size. But that's not all - most, if not all, of the Class 3 hitches are designed to be mounted on SUVs. I'd imagine that the unibody construction of most cars is of insufficient strength to take the load, especially if the load bounces, like the cantilevered load of 5 bikes will do. Check out e-trailer.com for carriers, hitches, and then match up your car to see what works.
You don't want to overload the car and cause body damage or lose the hitch or carrier and the 5 bikes on it. Good luck with your search - you might end up with some bikes on the back of the car and the rest on the roof.