Urban rail transit is one of the primary systems for urban transportation capacity. With the increasing demand for the development of smart cities in recent years, the design, research, and optimization of smart rail transit systems have become the research direction and focus for many scholars. Smart rail transit systems require trains to have intelligent computing power to meet a variety of intelligent service needs. Due to the numerous limitations of on-board equipment in trains, it is not practical to deploy high-performance computing devices on them, hence the need to introduce other devices to provide computational support. This study, aimed at the special scenarios of smart rail transit systems, designs a cloud-edge collaborative computing architecture for intelligent tasks based on 5G and edge intelligence. The resource allocation process in this architecture is mathematically modeled and transformed into an optimization problem that minimizes task latency. To solve this optimization problem, this paper employs a discrete stochastic approximation algorithm to minimize the total processing delay of tasks in the smart rail transit system. Simulation results indicate that the algorithm can effectively reduce the processing delay of intelligent tasks in smart rail transit systems.