This paper focuses on the strategies that employ the fifth generation (5G) wireless networks in the optimal management of demand-side response in the future energy systems with the high penetration of renewable energy sources (RES). It also provides a comparison between advantages and challenges of 5G networks in demand-response renewable energy grids. Large-scale renewable energy integration always leads to a mismatch between generation and load demand in the short run due to the intermittency. It is often envisioned that 5G wireless networks that were recently launched and would most likely be fully deployed worldwide by 2035 would bring many technological and economic benefits for a plethora of the future high-renewables grids featuring electric transport and heating as well as prosumers generating renewable energy and trading it back to the grid (for example, in the vehicle-to-grid (V2G) framework) and among themselves using peer-to-peer (P2P) networks. Our paper offers a comprehensive analysis of 5G architecture with the perspectives of optimal management of demand-side response in the smart grids of the future. We show that the effective deployment of faster and more reliable wireless networks would allow faster data transfers and processing, including peer-to-peer (P2P) energy trade market, Internet of Vehicles (IoV) market, or faster smart metering, and thence open the path for the full-fledged Internet of Energy (IoE). Moreover, we show that 5G wireless networks might become in the future sustainable energy systems paving the road to even more advanced technologies and the new generations of networks. In addition, we demonstrate that for the effective management of energy demand-side response with a high share of renewables, certain forms of governments funding and incentives might be needed. These are required to strengthen the support of RES and helping to shift to the green economy.