To support the delay-bounded multimedia services for 5G mobile wireless networks, the statistical quality-of-service (QoS) technique has been developed to jointly guarantee statistically delay-bounded video transmissions over different timevarying wireless channels, simultaneously. On the other hand, as one of the 5G promising candidate techniques, energy harvesting (EH) is designed to solve the energy supply problem while bringing new challenges due to the stochastic nature of the harvested energy in supporting the heterogeneous statistical delay-bounded QoS provisionings. However, due to the unknown dynamics of the distributions for energy and data arrival processes, it is challenging to design the optimal EH and resource allocation policies under the heterogeneous statistical delay-bounded QoS constraints. Towards this end, the reinforcement learning algorithms have been designed to find the optimal EH and resource allocation policies by allowing the mobile users to learn from the different network states and historical behaviors until the optimal response set is reached. To overcome the aforementioned problems, in this paper we propose the learning based algorithm for designing the optimal EH and resource allocation policies while satisfying the heterogeneous statistical delay-bounded QoS constraints over EH based 5G mobile wireless networks. In particular, we establish the EH based system model. Under the heterogeneous statistical delay-bounded QoS requirements, we formulate the effective-capacity optimization problem over EH based 5G mobile wireless networks. Then, we apply the learning based EH algorithm for deriving the optimal resource allocation policy. Also conducted is a set of simulations which validate and evaluate the system performances and show that our proposed learning based EH scheme outperforms the other existing schemes under the heterogeneous statistical delay-bounded QoS constraints over 5G mobile wireless networks.