The fifth generation of mobile communication networks (5G) is foreseen to be a key enabling technology for the fourth stage of the industrial revolution, commonly termed as “Industry 4.0”. Future Smart Factories envisioned in that context will leverage Industry 4.0 and 5G technology to increase flexibility and efficiency of the manufacturing processes, thus ensuring global competitiveness of industrial manufacturing. While 5G technologies such as network slicing may accommodate industrial applications in public networks, Private 5G Networks, operating locally and highly optimized towards specific applications, are a disruptive emerging approach to meet the specific demands of industrial use cases. Building on the premise of Private 5G Networks, the 5G CONNI project aims at providing an integrated end-to-end 5G test and demonstration network for industrial applications, leveraging current results from standardization and related research projects. Major contributions of the project consist in the definition of new Private 5G Network architectures and operator models, measurements and tools for application specific network planning, tuning and monitoring and the development of innovative new technologies and enabling components in the context of URLLC radio communication, mobile edge computing, core network design and joint optimization of these components. The project will set up two interconnected industrial trial sites in manufacturing facilities in both, Europe and Taiwan. At these sites, selected use cases will be realized and integrated into an end-to-end industrial Private 5G Network demonstrator. This will be used for technology verification and a thorough KPI analysis. The project results will be reflected back into the relevant standardization bodies and industry fora and used as an input for regulatory institutions in both Europe and Taiwan in order to shape the requirements for the operation of private networks.