3G and 4G have brought higher data speeds and efficiency, the hopes for 5G are much broader: Speed and efficiency, yes, but also substantial latency reduction and much improved robustness for vital applications such as telemedicine and self-driving cars, support for many more connected devices, and the ability to support a "seamlessly connected society" - people, their data and applications, the cloud, things, transport networks and so on.
Research is being conducted now under the "IMT-2020" banner, still focused on identifying 5G use cases and requirements, enabling technologies and spectrum requirements.