Digitalization and networking are taking on an increasingly important role in manufacturing. Fifth Generation mobile networks (5G) allow us to wirelessly connect multiple assets in factories with guaranteed quality of service (QoS). A 5G non-public network (5G-NPN) realizes a dedicated network with secure communication within the factory. Time-sensitive networking (TSN) provides deterministic connectivity and reliability in local networks. Edge computing moves computing power near factory locations, reducing the latency of edge applications. Making production processes more flexible, more robust, and resilient induces a great challenge for integrating these technologies. This paper presents the benefits of the joint use of 5G-NPN, TSN, and edge computing in manufacturing. To that end, first, the characteristics of the technologies are analyzed. Then, the integration of different 5G-NPN deployment options with edge (and cloud) computing is presented to provide end-to-end services. For enhanced reliability, ways of interworking between TSN and edge computing domains are proposed. Afterward, as an example realization of edge computing, the investigation on the capabilities of the Kubernetes container orchestration platform is presented together with the gap analysis for smart manufacturing requirements. Finally, the different integration options, interworking models, and Kubernetes-based edge computing are evaluated to assist smart factories to use these new technologies in combination in the future.