Due to the ever-increasing requirements of delay-sensitive and mission-critical applications in 5G, mobile edge computing is promising to react and support real-time interactive systems. However, it is still challenging to construct a 5G-enabled traffic management system, owing to the qualification of ultra-low latency and ubiquitous connectivity. Furthermore, the computing resources and storage capacities of edge nodes are limited, thus computation offloading is a fundamental issue for real-time traffic management. This paper puts forward a hybrid computation offloading framework for real-time traffic management in 5G networks. Specially, we consider both nonorthogonal-multiple-access-enabled and vehicle-to-vehicle-based traffic offloading. The investigated problem is formulated as a joint task distribution, subchannel assignment, and power allocation problem, with the objective of maximizing the sum offloading rate. After that, we prove its NP-hardness and decompose it into three subproblems, which can be solved iteratively. Performance evaluations illustrate the effectiveness of our framework.