How much natural background radiation is there at 5g radio frequencies?
"5G frequencies" do not exist. 

5G is just a marketing term. All LTE things after release 14 (I think) is called 5G. So, your LTE base station, if it had a software update, is a 5G station, occupying the exact same spectrum as before.

So, there's potentially 5G wherever you find LTE; depending on your country, that might be somewhere between 800 MHz and 3000 MHz. You'll have to consult with your mobile network operator to learn which bands they bought a license to operate in and are using.

You practically get no background radiation on microwave frequencies. Receiver noise is practically always dominated by receiver-side Johnson-Nyquist noise.

We can compare a lot of the LTE frequencies with what they were used for before reassignment: TV whitespace. Now, a typical TV transmitter has some 75 to 200 kW of power, and around 6 dBi of gain (so it doesn't illuminate the sky). The rest is free-space path loss. A LTE base station doesn't have a constant transmit power, but transmit as much as necessary to each phone as necessary to deliver the quality of service it needs. That means it transmits 0 W to maybe 500 W. I don't have actual numbers – the power budget of base stations is what makes up a significant (if not the most significant) part of the cost of operating a cellular network, and operators tend to be a bit tightly knit when it comes to their business calculations, as that's knowledge that their competitors could use to push exactly into the niches that they don't fully occupy.

ATSC assumes a minimum of -68 dBm received power at the TV for minimal functionality. NTSC/PAL/SECAM is practically more in the -55 dBm range. Notice that this is a continuous illumination; you're constantly exposed to that.

LTE works with -100 dBm quite solidly. For higher rates, bursts of -70 dBm to -50 dBm are desirable. But this is only when there's acute usage. And of course, the cell phone's transmit power in your hand totally trumps your received signal power (for obvious distance reasons):

The square power law applies; if your signal has to reach further by a factor of \$x\$ while maintaining identical receive power, your transmit power has to go up by \$x^2\$. 

Corollary, the more cell towers a populated area has, the lower the average person's exposure: to deliver a fixed signal quality, the transmitter has to use quadratically less power, the closer the communication partner is. This applies to both handset and tower.


Aside from the minor technical changes with respect to the wave form between 4G and 5G, there's also the practically nowhere deployed 5G NR (new radio), a standard that specifies optional connectivity on a ca 60 GHz carrier.

That's not something you'll find on a cell tower - 60 GHz really propagates pretty much like light, is heavily attenuated by atmosphere and especially atmospheric moisture, so it's not technology that's useful to mount on a tower. It's for indoor and subway / street "canyon" situations. Powers are in the regions you'd call "laughably low", think nanowatts emitted power. Building efficient 60 GHz amplifiers is still a hard task. 

Also, I know not a single person that has a phone that has a phone that supports 60 GHz yet.