Future Smart Factories will leverage Industry 4.0 and 5G technology to increase both flexibility and efficiency of manufacturing processes, thus ensuring global competitiveness of industrial manufacturing. 5G technologies such as network slicing may accommodate industrial applications in public networks, while Private 5G Networks, operating locally and being highly optimized towards specific applications, may require disruptive technologies to meet the specific and challenging industrial use cases requirements. The 5G CONNI Europe-Taiwan project investigates innovative solutions for Private 5G and beyond Network. This includes the definition of new architectures and measurements tools as well as, the development of innovative technologies and their enabling components in the context of mobile edge assisted URLLC. Building on the premise of Private 5G Networks, the 5G CONNI project will offer an unprecedented integrated end-to-end 5G testing network for testing specifically industrial applications in accordance with updated 5G standardization specifications. The 5G CONNI project will validate its innovative and technologically advanced solutions and components with a real-field cross-continental end-to-end industrial Private 5G Network demonstration between two interconnected industrial manufacturing sites in Taiwan and in Europe.