As mobile broadband subscriptions grow twice as fast as the fixed ones and the Internet of Things comes forth, the 5G vision of the Internet of Everything (people, devices, and things), becomes a substantial and credible part of the near future. In this paper, we argue that the 5G vision is still missing a fundamental concept to realize its societal promise: the Internet of EveryOne (IoEO), i.e., means and principles to overcome the concerns that the current 5G perspective raises for the digital divide and the network neutrality principle. We discuss open-source software and hardware, Community Networks, mobile edge computing and blockchains as enablers of the IoEO and highlight open research challenges with respect to them. The ultimate objective of our paper is to stimulate research with a short-term, lasting impact also on that 50% (or more!) of population that will not enjoy 5G anytime soon.