Basically, 5G introduces some new technology that increases the so called spectral efficiency (bps/hz) that is how much tput you can deliver over the allocated spectrum. 5G introduces things like mm-wave tech using phased array antennas, better massive MIMO etc.

But even with the tech, it's probably not enough to handle the demand they are hoping for, hence they spectrum buying spree they have been on lately.

It goes back to the Shannon law talked about here, you either have to build more cells to make the signal better (better signal lets you pack more bps per hz, or you need more spectrum. Both are expensive, and most of them are doing both.