Fifth-generation (5G) networks consist of relatively smaller cells compared to legacy networks. Therefore, a user will take a shorter time toward the cell edge. This exposes the mobile station (MS) to frequent handovers, which are bottlenecks affecting the quality of service and user experience. In this study, we introduce a self-optimization method for three pivotal handover control parameters (HCPs): Threshold, Hysteresis and Time-To-Trigger. The proposed approach considers a holistic range of factors to determine the optimal values for these HCPs. These factors include the received power of reference signals (channel conditions), the speed and direction of the user (mobility profile), and the synchronization signal periodicity and handover procedure latency (representing system parameters). Through analytical deliberations, the study establishes a framework for achieving optimal HCPs to minimize the handovers, mitigate the ping-pong effects, reduce handover failures, and sustain a good throughput performance. Furthermore, considering the channel, user, and system parameters allowed cell-specific HCP optimization, enabling the implementation of this method with any of the measurement events outlined in the 3rd Generation Partnership Project (3GPP) release 16 for 5G. This study shows that concurrent self-optimization of Threshold, Hysteresis, and Time-To-Trigger can yield remarkable enhancement of handover performance.