The ubiquitous and deterministic communication systems are becoming indispensable for future vertical applications such as industrial automation systems and smart grids. 5G-TSN (Time-Sensitive Networking) integrated networks with the 5G system (5GS) as a TSN bridge are promising to provide the required communication service. To guarantee the end-to-end (E2E) QoS (Quality of Service) performance of traffic is a great challenge in 5G-TSN integrated networks. A dynamic QoS mapping method is proposed in this paper. It is based on the improved K-means clustering algorithm and the rough set theory (IKC-RQM). The IKC-RQM designs a dynamic and load-aware QoS mapping algorithm to improve its flexibility. An adaptive semi-persistent scheduling (ASPS) mechanism is proposed to solve the challenging deterministic scheduling in 5GS. It includes two parts: one part is the persistent resource allocation for timesensitive flows, and the other part is the dynamic resource allocation based on the max-min fair share algorithm. Simulation results show that the proposed IKC-RQM algorithm achieves flexible and appropriate QoS mapping, and the ASPS performs corresponding resource allocations to guarantee the deterministic transmissions of time-sensitive flows in 5G-TSN integrated networks.