In recent years, energy efficiency has become a major cause of concern in mobile networks. The overwhelming applications and services provided by the evolving fifth‐generation (5G) technologies consume a substantial amount of energy, especially at the user equipment (UE). The 3rd Generation Partnership Project has proposed discontinuous reception (DRX) as a power saving technique for the UE. The DRX protocol has been used by different generation mobile standards. In this paper, the performance of hybrid directional DRX (HD‐DRX) for 5G communication with beam searching is improved upon by augmenting intermediate single packet active states in the short and long sleep cycles for light traffic in 5G networks. The supplementary active states save power by allowing the UE to receive packets within the sleep periods up to a certain threshold without transitioning to the active state. The short bursts of packets in the light traffic are received directly through the intermediate active states without beam searching. Once the given threshold exceeds, the system functions as normal HD‐DRX for the heavy traffic without the intermediate states. The proposed model is analyzed as a semi‐Markov process with the bursty packet data traffic model. The numerical results of the proposed model show 3.1% improvement in power saving and reduction in average delay by around 2.5 s compared to the HD‐DRX. Further studies can help deep dive into operationalizing this on a mass scale.