Content caching on the edge of 5G networks is an emerging and critical feature to quench the thirst for content of future connected cars. However, the tight packaging of 5G cells, the finite storage capacity at the edge, and the need for content availability while driving motivate the need to develop smart edge caching strategies adapted to the mobility characteristics of connected cars. In this paper, we propose a scheme called RICH (RoadsIde CacHe), which optimally caches content at edge nodes where connected vehicles require it most. In particular, our scheme is designed to ensure in-order delivery of content chunks to end users. Unlike blind popularity decisions, the probabilistic caching used by RICH accounts for the user mobility information that the system can realistically acquire. Furthermore, we provide a complete system architecture and define the protocols through which the different system entities can interact. We assess the performance of our approach against state-of-the-art solutions, under realistic mobility datasets and system scenarios. Our RICH edge caching scheme improves significantly the content availability at the caches and reduces the required backhaul bandwidth, with beneficial effects for both the end users and the network operators.