The multi-tier heterogeneous structure of 5G with dense small cells deployment, relays, and device-to-device (D2D) communications operating in an underlay fashion is envisioned as a potential solution to satisfy the future demand for cellular services. However, efficient power allocation among dense secondary transmitters that maintains quality of service (QoS) for macro (primary) cell users and secondary cell users is a critical challenge for operating such radio. In this paper, we focus on the power allocation problem in the multi-tier 5G network structure using a non-cooperative methodology with energy efficiency consideration. Therefore, we propose a distributive intuition-based online learning scheme for power allocation in the downlink of the 5G systems, where each transmitter surmises other transmitters power allocation strategies without information exchange. The proposed learning model exploits a brief state representation to account for the problem of dimensionality in online learning and expedite the convergence. The convergence of the proposed scheme is proved and numerical results demonstrate its capability to achieve fast convergence with QoS guarantee and significant improvement in system energy efficiency.