Ensuring a reliable and stable communication throughout the mobility of User Equipment (UE) is one of the key challenges facing the practical implementation of the Fifth Generation (5G) networks and beyond. One of the main issues is the use of suboptimal Handover Control Parameters (HCPs) settings, which are configured manually or generated automatically by certain self-optimization functions. This issue becomes more critical with the massive deployment of small base stations and connected mobile users. This will essentially require an individual handover self-optimization technique for each user individually instead of a unified and centrally configured setting for all users in the cell. In this paper, an Individualistic Dynamic Handover Parameter Optimization algorithm based on an Automatic Weight Function (IDHPO-AWF) is proposed for 5G networks. This algorithm dynamically estimates the HCPs settings for each individual UE based on UE's experiences. The algorithm mainly depends on three bounded functions and their Automatic Weights levels. First, the bounded functions are evaluated, independently, as a function of the UE's Signal-to-Interference-plus-Noise-Ratio (SINR), cells' load and UE's speed. Next, the outputs of the three bounded functions are used as inputs in a new proposed Automatic Weight Function (AWF) to estimate the weight of each output bounded function. After that, the final output is used as an indicator for optimizing HCPs settings automatically for a specific user. The algorithm is validated throughout various mobility conditions in the 5G network. The performance of the analytical HCPs estimation method is investigated and compared with other handover algorithms from the literature. The evaluation comparisons are performed in terms of Reference Signal Received Power (RSRP), Handover Probability (HOP), Handover Ping-Pong Probability (HPPP), and Radio Link Failure (RLF). The simulation results show that the proposed algorithm provides noticeable enhancements for various mobile speed scenarios as compared to the existing Handover Parameter Self-Optimization (HPSO) algorithms.