Nowadays, at least two billion people are experiencing a complete lack of wireless cellular network coverage. These users live in rural areas and low-income regions, where network operators are not keen to invest, mainly due to high capital expenditure and operational expenditure costs, as well as the scarcity of electricity from the grid. We tackle this challenge by proposing a 5G network explicitly designed to serve rural and low-income areas. Our solution investigates the possibility of mounting remote radio heads on top of unmanned aerial vehicles, as well as large cells (LCs) to increase the coverage range. In addition, 5G nodes are powered by solar panels and batteries. Preliminary results, obtained over three representative case studies located in Italy, Cook Islands, and Zimbabwe, show that providing connectivity in rural and low-income areas by means of the proposed 5G architecture is feasible. At the same time, we also show that the monthly subscription fee paid by the users can be kept sufficiently low, that is, less than €1/month in low-income areas, and around €11/month in rural regions.