Prior cell phone use causing little or no cancer causing effect is well established. But effects of prior technologies is not a good predictor of effects of the new technologies.
A perfect analogy is: You have been touching the outside of the tea kettle for years, and you never got burn. Now you replaced it with a brand new tea kettle that delivers hotter water with a different technology. Are you sure you will not get burn touching the outside of this new kettle because touching the old one was fine?
With EM waves, frequency is energy. Higher the frequency, the more the energy. In the last 30 years of cell phone, it was not much more than 2GHz. With true 5G, when fully implemented, it will be much higher frequency (20+ GHz) and directionally focused (it will not decrease by the square of distance).
20+ GHz is getting nearer to the point where the individual photons (energy packets) can cause some damage to a molecule - getting there but not that strong as compare to say dental X Ray which would be over a billion times higher in frequency (energy per photon). Add to that, cell signals are weak (fewer photons). So, photons (packets of energy) from the 5G tower may wiggle your DNA molecules a bit but knocking your DNA molecules out of shape is not a worry.
That said, your body is absorbing the energy, a more focused and "hotter" beam more energetic than the weak 2G/3G/4G signals. What is the effect of heating say the temple area of your brain (which is where your phone is when the speaker is at your ear). What if you just heat it a little bit let it cool, and do it again; Day in, day out, again and again. There is no study out there (I know of) that says it will definitely cause harm, nor is there a study out there (I know of) that says it will definitely NOT cause harm.
Life is full of risks. Just walking down the street to a pizza joint is risk - a truck tire may blow and you got hit by a piece of rubber that fracture your skull - dying over a bite of pepperoni and cheesed. But we never worry that much about rubber shooting out of a blown tire walking around town. So, why should 5G be any different. Nothing is risk free. 5G EM waves, or the damn truck passing by...
Personally, I worry a lot more about the lost of privacy than the risk of cancer by these new generation of phones.