Recently, discontinuous reception mechanisms (DRX) and wake-up schemes (WuS) have been proposed to enhance the energy efficiency of 5G mobile devices and prolong the battery lifetime. The existing DRX and WuS use commonly pre-configured parameters that cannot be adjusted dynamically. In this paper, a novel wake-up scheduling (WuSched) concept is introduced to further improve the energy efficiency of WuS-enabled mobile devices while controlling the buffering delay in a dynamic manner. The main idea of WuSched is to use a fixed configuration of the wake-up scheme and adjust the scheduling of the wake-up signals dynamically based on actual traffic arrivals. For this purpose, two different optimization approaches of the wake-up scheduling concept are proposed, analyzed, and compared, namely offline and online wake-up schedulers (WuSched-Offline and WuSched-Online). First, the WuSched-Offline is analyzed analytically for Poisson traffic arrivals and optimized (offline) to balance the average delay and power consumption. Second, the WuSched-Online is proposed to take online decisions based on traffic prediction, which is able to deal with general and more complex traffic models. Towards this end, we develop a framework for the prediction of packet arrivals based on recurrent neural networks. Numerical results show that both wake-up schedulers outperform the ordinary WuS-based system where wake-up scheduler is not deployed. In particular, for predefined delay requirements of video streaming, audio streaming, and mixed traffic flow, the WuSched-Online reduces the power consumption of the baseline WuS by up to 36%, 28% and 9%, respectively. Results also show that the WuSched-Offline has slightly better energy efficiency than the WuSched-Online in the case of Poisson packet arrivals, as it is optimized for that, while its power consumption is slightly higher than that of the WuSched-Online scheduler for realistic traffic scenarios.