Internet has shown itself to be a catalyst for economic growth and social equity but its potency is thwarted by the fact that the Internet is off limits for the vast majority of human beings. Mobile phones---the fastest growing technology in the world that now reaches around 80% of humanity---can enable universal Internet access if it can resolve coverage problems that have historically plagued previous cellular architectures (2G, 3G, and 4G). These conventional architectures have not been able to sustain universal service provisioning since these architectures depend on having enough users per cell for their economic viability and thus are not well suited to rural areas (which are by definition sparsely populated). The new generation of mobile cellular technology (5G), currently in a formative phase and expected to be finalized around 2020, is aimed at orders of magnitude performance enhancement. 5G offers a clean slate to network designers and can be molded into an architecture also amenable to universal Internet provisioning. Keeping in mind the great social benefits of democratizing Internet and connectivity, we believe that the time is ripe for emphasizing universal Internet provisioning as an important goal on the 5G research agenda. In this paper, we investigate the opportunities and challenges in utilizing 5G for global access to the Internet for all (GAIA). We have also identified the major technical issues involved in a 5G-based GAIA solution and have set up a future research agenda by defining open research problems.