Since the Information & Communications Technologies (ICT) were designed without taking the energy-saving into account, the unexpected excessive energy consumption of the fourth-generation (4G) and pre-4G wireless networks causes serious carbon dioxide emissions. To achieve green wireless networks, the fifth-generation (5G) wireless networks are expected to significantly increase the network energy efficiency while guaranteeing the quality-of-service (QoS) for time-sensitive multimedia wireless traffics. In this paper, we develop the statistical delay-bounded QoS driven green power allocation schemes to maximize the effective power efficiency (EPE), which is defined as the statistical-QoS-guaranteed throughput (effective capacity) per unit power, over single-input single-output (SISO) and multipleinput multiple-output (MIMO)-channels based 5G mobile wireless networks. For the SISO-channel based 5G wireless networks, our developed QoS-driven green power allocation scheme converges to the despicking water-filling scheme (despicking channel inversion scheme) when the QoS constraint becomes very loose (stringent). This scheme and its analyses can be also extended to the diversity-based MIMO wireless networks, but not to the multiplexing-based MIMO wireless networking systems. To this end, we also further develop and analyze the statistical-QoSdriven green power allocation scheme to maximize the EPE over the multiplexing-MIMO based 5G mobile wireless networks. The obtained numerical results show that our developed statistical QoS-driven green power allocation schemes can optimize the EPE over 5G mobile wireless networks, thus enabling the effective implementation of green 5G wireless networks.