The rolling-out of 5G antennas over the territory is a fundamental step to provide 5G connectivity. However, little efforts have been done so far on the exposure assessment from 5G cellular towers over young people and “sensitive” buildings, like schools and medical centers. To face such issues, we provide a sound methodology for the numerical evaluation of 5G (and pre-5G) downlink exposure over children, teenagers, schools and medical centers. We then apply the proposed methodology over two real scenarios. Results reveal that the exposure from 5G cellular towers will increase in the forthcoming years, in parallel with the growth of the 5G adoption levels. However, the exposure levels are well below the maximum ones defined by international regulations. Moreover, the exposure over children and teenagers is similar to the one of the whole population, while the exposure over schools and medical centers can be lower than the one of the whole set of buildings. Finally, the exposure from 5G is strongly lower than the pre-5G one when the building attenuation is introduced and a maturity adoption level for 5G is assumed.