Theoretically some do, but it really depends on where in the country you're located and your carrier. For instance, based on
this list of owned spectrum and
this calculator, AT&T is possibly able to do 979mbps downloads (aggregating 1 B4, 1 B66, 1 B12 and 1 B2 carrier) with 4x4 MIMO and 256QAM if they get rid of 3G/UMTS. This isn't taking into account the possible usage of LTE-U (unlicensed 5GHz spectrum, i.e. the same as used for Wi-Fi), either.
Also, even if spectrum constrained, a single 20MHz carrier gives you a maximum theoretical downlink speed of 391.6mbps. While all the speeds mentioned are unlikely to be met in real life, I imagine with enough cell density, one could get to a significant fraction of theoretical a large amount of the time. That said, most people's experiences on US carriers involve double-digit download speeds (which are still reasonable for the vast majority of mobile phone use, mind you, just not so much the other potential uses that 5G supposedly enables).
In any case, more spectrum does make reaching those speeds more consistently with fewer towers a lot easier. Which, since T-Mobile recently got a whole bunch of it, should put them in a pretty good position for 5G.