While 5G has rolled out since 2019 and exhibited versatile advantages, its performance under high/extreme mobility scenes (e.g., driving, high-speed railway or HSR) remains mysterious. In this work, we carry out a large-scale field-trial campaign, taking >13,000 Km round-trips on HSR moving at 250-350 Km/h, with operational 5G cellular coverage along the railway. Our empirical study reveals that coupling interaction among high mobility, 5G handover characteristics, and applications' sluggish reaction to handover, results in catastrophic damage to user experience: low TCP bandwidth utilization of 26.6% and glitchy 4K VoD streaming. To solve the problem, we propose an edge-assisted mobility management framework called Octopus. Different from previous works, Octopus aims at a standard-compatible and easy-to-deploy solution, thus we take a new design paradigm of exploiting the edge intelligence on multi-access edge computing (MEC). We realize Octopus as a universal MEC service ready for benefiting any third-party mobile applications. We prototype, deploy, and evaluate Octopus in operational 5G, which demonstrates the significant performance gain across the full-range mobile scenarios, e.g., HSR, driving, and walking.