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. The goal of this article is therefore to provide a sound methodology for the numerical evaluation of 5G (and pre-5G) exposure over children, teenagers, schools and medical centers. Our results, obtained by applying the proposed methodology in two realistic scenarios, reveal that the exposure from 5G cellular towers will increase in the forthcoming years, in parallel with the growing adoption levels of 5G. However, the observed 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 also lower than the one of the whole set of buildings. Finally, when the building attenuation is introduced, the exposure from 5G is strongly lower the the pre-5G one, even for a maturity adoption level of 5G.