Would physics allow us to build a really big airplane, say 5x the size of a standard airliner?

 The way an airplane gets into air is not very complicated. If it can create enough lift by accelerating air over the wings and overcome its weight, it will fly.

I would assume you want to make an airplane five times as large as the current largest airplane, the Antonov An-225. Well, the engines we currently have are going to be of no use. So, you would need to come up with an engine design that will create enough thrust to push the airplane. Of course, you could attach more engines on the wings, but that would mean, the wings has to be made stronger and stiffer to overcome the stress from the engines. More stronger means more materials that has to be shoved into it. This would increase the overrall mass of the airplane, something we really want to reduce.

The wings are going to be a major weak point. This very large airplane will require quite an enormous one. This wing has to be sturdy enough to be perfectly fitted into the fuselage. In flight, the wings are usually pulled up and down by the changes in lift force. As a bigger wing has to be quite rigid it will give up very easily. Wing flexibility is important to counter these very undesirable forces.