The deployment of 5G wireless communication services requires the installation of 5G next-generation Node-B Base Stations (gNBs) over the territory and the wide adoption of 5G User Equipment (UE). In this context, the population is concerned about the potential health risks associated with the Radio Frequency (RF) emissions from 5G equipment, with several communities actively working toward stopping the 5G deployment. To face these concerns, in this work, we analyze the health risks associated with 5G exposure by adopting a new and comprehensive viewpoint, based on the communications engineering perspective. By exploiting our background, we analyze the alleged health effects of 5G exposure and critically review the latest works that are often referenced to support the health concerns from 5G. We then precisely examine the up-to-date metrics, regulations, and assessment of compliance procedures for 5G exposure, by evaluating the latest guidelines from IEEE, ICNIRP, ITU, IEC, and FCC, as well as the national regulations in more than 220 countries. We also thoroughly analyze the main health risks that are frequently associated with specific 5G features (e.g., MIMO, beamforming, cell densification, adoption of millimeter waves, and connection of millions of devices). Finally, we examine the risk mitigation techniques based on communications engineering that can be implemented to reduce the exposure from 5G gNB and UE. Overall, we argue that the widely perceived health risks that are attributed to 5G are not supported by scientific evidence from communications engineering. In addition, we explain how the solutions to minimize the health risks from 5G are already mature and ready to be implemented. Finally, future works, e.g., aimed at evaluating long-term impacts of 5G exposure, as well as innovative solutions to further reduce the RF emissions, are suggested.