This paper presents a novel QoS and mobile cloud and fog computing framework for future fifth generation (5G) of mobile and fixed nodes with radio network aggregation capability. The proposed 5G framework is leading to high QoS provisioning for any given multimedia service, higher bandwidth utilization, traffic load sharing, mobile cloud plus fog computing features, and multi-radio interface capabilities. The framework is user-centric, targeted at always-on connectivity with using radio network aggregation for available mobile broadband connections, and empowered with mobile cloud and fog computing advantages. Moreover, our proposed framework is using Lyapunov drift-plus-penalty theorem that provides a methodology for designing algorithm to maximize the average throughput and stabilize the queuing. Also, we are showing the upper bound of the consumed power and the lower bound of the battery lifetime for the proposed 5G terminal. The advanced performance of our 5G QoS plus MCC framework is evaluated using simulations and analysis with multimedia traffic in heterogeneous mobile and wireless environment. The simulation results are showing that the maximal network utilization, maximal throughput, minimal end-to-end delay, efficient energy consumption, and other performance improvements are achieved.