The big picture of 5G will bring a range of new unique service capabilities, where ensuring Quality of Experience (QoE) continuity in challenging situations such as high mobility, e.g. on-board User Equipments (UEs) in High Speed Train (HST) is one of sharp killer applications. In this paper, we propose a Mobile Edge Computing (MEC) driven solution to improve QoE, for UEs in the HST with perceived Dynamic Adaptive Streaming over HTTP (DASH) video demands. Considering the challenging wireless communication conditioning (e.g., path loss and Doppler Effect due to high mobility) between HST and Base Station (BS) along the railway for enabling progress and seamless video consuming, the case study shows the benefit of MEC functions mainly from content prefetching and complementarily from content caching, over benchmark solution where UEs solely download video segments through challenging wireless channel.