The fifth generation of wireless communications networks (5G) offers high quality of services (QoSs). The higher QoSs, the higher data rate and power consumption are essentially required. Then, battery charge is consumed by 5G UE devices. To solve this issue, the hybrid directional system was introduced in 5G communications under existence of mmWave beam air interface. Hybrid Directional Discontinuous Reception (HD-DRX) sleep mode mechanism was presented in order to absorb energy consumed by UE battery. In this article, the proposed algorithm is the additional active states to each DRX sleep cycle of the original HD-DRX (4-states) model. A proposed Semi-Markov chain is utilized to describe HD-DRX (5-states) and HD-DRX (6-states) models. These both proposed models enhance the power saving factor and average delay compared to the original HD-DRX (4-states) model. A MATLAB simulation program is used to validate the numerical analysis. Accurate results for power saving factor and average delay are provided.