Industry 4.0, artificial intelligence, and the Internet of Things are fundamental technological advances for the development of smart manufacturing. A properly designed network infrastructure is an important solution for making the manufacturing and logistics processes more flexible, autonomous and efficient. The 5G communications standard opens up important new perspectives for the deployment of industrial private networks. This paper has considered the main problems encountered in traditional networks for deploying smart manufacturing. We have presented a 5G network architecture based on the latest technologies, such as non-orthogonal multiple access, SDN, NFV and cloud computing. The use of these technologies in combination with network slicing provides high reliability and security of the communication channels of industrial networks, as well as stability and isolation from external public networks. For this purpose, we have developed a new method for the dynamic radio resource management between the network slices, taking into account their importance. We developed a method for prioritizing radio resources within a slice, considering the importance of industrial services. We proved that the proposed methods provide ultra-low latency and high reliability for priority messages in the industrial 5G network.