Next generation 5G wireless networks envision innovative radio technologies for ultra dense deployment with improved coverage and higher data rates. However, the deployment of ultra dense 5G networks, with relatively smaller cells, raises significant challenges in network energy consumption. Emerging green cloud radio access networks (C-RANs) are providing assurance of energy efficient cellular operations for reduction of both greenhouse emissions and operators’ energy bill. Cellular traffic dynamics play a significant role in efficient network energy management. In this paper, we first identify the complexity of the optimal traffic awareness in 5G C-RAN and design a framework for traffic-aware energy optimization. The virtual base station cluster (VBSC) of C-RAN exploits an information theoretic approach to model and analyze the uncertainty of cellular traffic, captured by remote radio heads (RRH). Subsequently, using an online, stochastic game theoretic algorithm, the VBS instances optimize and learn the cellular traffic patterns. Efficient learning makes the C-RAN aware of the near-future traffic. Traffic awareness helps in selective switching of a subset of RRHs, thus reducing the overall energy consumption. Our VBS prototype implementation, testbed experiments, and simulation results, performed with actual cellular traffic traces, demonstrate that our framework results in almost 25% daily energy savings and 35% increased energy efficiency with a negligible overhead.