With the rapid developments of fifth generation (5G) mobile communication networks in recent years, different use cases can now significantly benefit from 5G networks. One such example is high-speed trains found in several countries across the world. Due to the dense deployment of 5G millimetre wave (mmWave) base stations (BSs) and the high speed of moving trains, frequent handovers (HOs) occur which adversely affect the Quality-of-Service (QoS) of mobile users. User association for load balancing is also a key issue in 5G networks. Therefore, HO optimisation and resource allocation are major challenges in the mobility management of high-speed train systems. Handover Margin (HOM) and Time-to-Trigger (TTT) parameters are crucial for the HO process since they affect the key performance indicators (KPIs) of high-speed train systems in 5G networks. To manage system performance from the aspect of predictive analytics, we have modelled system performance of mobility management through machine learning (ML). First, the HO management process of a high-speed train scenario is framed as a supervised ML problem. The inputs for the problem are regression task, HOM and TTT and the outputs are key performance indicators (KPIs). Second, data processing is accomplished after generating a simulation dataset. Several methods are employed for the dataset, such as Adaptive Boosting (AdaBoost), Gradient Boosting Regression (GBR), CatBoost Regression (CBR), Support Vector Regression (SVR), Multi-layer Perceptron (MLP), Kernel Ridge Regression (KRR) and K-Nearest Neighbour Regression (KNNR). Tenfold cross validation is then applied for choosing the best hyperparameters. Finally, the deployed methods are compared in terms of the Mean Absolute Error (MAE), Mean Square Error (MSE), Maximum Error (Max E), and R2 score metrics. From the MAE results, CBR achieves the best outcomes for load level and throughput KPIs with 0.003 and 0.0144, respectively. On the other hand, GBR achieves the best results for call dropping ratio (CDR), radio link failure (RLF) and spectral efficiency KPIs with 0.354, 0.082 and 0.354, respectively. CBR also follows GBR for the three KPIs with 0.356, 0.082 and 0.357, respectively. Only a slight difference in estimations is present. MLP achieves the best results for HO ping-pong (HOPP) and HO probability (HOP) KPIs with 0.0045 and 0.011, respectively. This is followed by GBR and CBR. From the MSE outcomes, CBR and GBR exhibit the best results for load level and throughput KPIs with 2e-5 and 3e-5, respectively. GBR attains the best results for CDR, RLF and spectral efficiency KPIs with 0.25, 0.011 and 0.025, respectively. Accordingly, CBR follows GBR with slightly different errors for the three KPI estimations. MLP achieves the best results for HOPP and HOP KPIs with 5e-5 and 3.6e-5, respectively. Again, this is followed by GBR and CBR for the estimation of these results. This indicates that CBR and GBR can capture relationships between inputs and KPIs for the dataset used in this study, outperforming all other methods generally used for solving this problem.