No, there are plenty of modern weather radars now that have nothing to do with 5 GHz. This is a good example of how the FCC managing spectrum is the furthest thing possible from a good allocation; trillions of economic activity are driven by use of unlicensed bands, yet because there is nobody in particular ready to put up billions for a slice of spectrum, we end up with the FCC "design by committee" process for releasing them. That means whoever happened to be there is considered some sort of "lifetime incumbent" that must be worked around at all costs, even if their use of prime spectrum is absurdly wasteful. Challenged with the choice between "incur $ costs on few" or "incur $$$ costs on many", the FCC will consistently pick "incur $$$$ on all".
This comment above is a good example of someone having stereotypes about RF administrations without actually knowing their field of expertise... It's not the matter of "unlicensed application don't pay license fees so administrations don't want them" (even though whenever you want to move an application out of a band, someone has to pay for the new equipment. But that's another topic and various countries have various process for that), but a matter of the laws of physics : various frequency bands have various physical properties and this applies not only to radio propagation but also (maybe more importantly) to measurements related to the molecules you want to observe. There are reasons why some bands and not others are dedicated to radars (and even more : some bands are fully passive because they are required for calibration and scientific measurements). So yes there are weather radars in other bands than 5 Ghz... so what ? Different radars measure different things and they are complementary (just like having different low/high bands for mobile operators are complementary for them). Before saying that the use of spectrum is "absurdly wasteful", you should show your thorough knowledge of the topic...
Keep in mind that whenever a new application appears, detailed technical analysis and simulations have to be done with regards to the other applications in co-channel and adjacent channel/bands, both with regards to direct interference, aggregated interference taking into account the projected density of the new spectrum use, clutter/terrain, propagation models, geometries of antennas, filter characteristics, etc. And even then, administrations do their best to find the right balance and enable as many applications as possible (including unlicensed and SRD), but those are tradeoffs and sometimes administration take risks to foster innovation (and sometimes it proves it was too permissive for the new user, such as what is happening now with regards to wifi vs weather radars).
(N.B. I am not in the US, but I guess FCC works similarly to EU administrations - which I know very well).
I certainly get why the FCC would tread lightly around "lifetime incumbents". In a civilized country people would look at the overall issues, recognize it as a collective problem, and support using shared money to reorganize things to society's long-term benefit. But in the US the incumbents would squawk about government overreach and creeping socialism and how President John Wayne gave their grandpappy that spectrum and it was their god-given right to use it without communist agitators trying to take it away, using taxpayer money to boot.
