With the advancement of Industry 4.0, the standardized integration of 5G and Time-Sensitive Networking (TSN) is set to play a crucial role in future factory environment. However, managing and scheduling integrated 5G-TSN network to ensure deterministic service for time-sensitive traffic has emerged as a significant research challenge. This paper proposes an joint optimization of traffic scheduling and routing for such integrated network. First, we design the system architecture of the 5G-TSN network, with the 5G system serving as a logical bridge to integrate into the TSN system. Then, we develop an greedy-genetic hybrid scheduling mechanism to address the joint optimization of routing and scheduling. Extensive experiments demonstrate that our proposed scheduling mechanism effectively ensures the deterministic transmission of time-sensitive traffic. Compared to benchmark algorithms, our approach achieves a superior scheduling success rate and average delay.