The fifth generation (5G) mobile communications system is envisioned to serve various mission-critical services such as industrial automation, cloud robotics, and safety-critical vehicular communications. To satisfy the stringent end-to-end latency requirement of these services, fog computing has been regarded as a promising technology to be integrated into 5G networks, in which computing, storage, and network functions are provisioned close to end users, thus significantly reducing the latency caused in transport networks. However, in the context of fog-computing-enabled 5G networks, the high mobility feature of users brings critical challenges to satisfy the stringent quality of service requirements. To address this issue, service migration, which transmits the associated services from the current fog server to the target one to follow the users' travel trace and keep the service continuity, has been considered. However, service migration cannot always be completed immediately and may lead to a situation where users experience a loss of service access. In this regard, low-latency service migration plays a key role to reduce the negative effects on services being migrated. In this paper, the factors that affect the performance of service migration are analyzed. To enable low-latency service migration, three main enabling technologies are reviewed, including migration strategies, low-latency, and high-capacity mobile backhaul network design, and adaptive resource allocation. Based on a summary of the reviewed technologies, we conclude that dynamic resource allocation is the worthiest one to research. Therefore, we carry out a use case, where reinforcement learning (RL) is adopted for autonomous bandwidth allocation in support of low-latency service migration in a dynamic traffic environment and evaluate its performance compared to two benchmarks. The simulation demonstrates that the RL-based algorithm is able to self-adapt to a dynamic traffic environment and gets converged performance, which has an obviously smaller impact on non-migration traffic than the two benchmarks while keeping the migration success probability high. Meanwhile, unlike the benchmarks, the RL-based method shows performance fluctuations before getting converged, which may cause unstable system performance. It calls for future research on advanced smart policies that can get convergence quickly, particularly for handling the migration of latency-sensitive services in 5G transport networks.