Wireless communication plays an important role in the digitization of industries. A 5G cellular communication system enables several industrial automation use cases. Fifth-generation deployments in industrial use cases have mainly been carried out in the sub-7 GHz frequency range. In this work, we empirically study 5G system performance in the millimeter wavelength (mmW) range for industrial use cases: additive manufacturing processes and precision manufacturing robotics. We carry out an experimental performance evaluation of a commercially available non-public 5G mmW system to assess its latency, reliability and throughput for uplink and downlink data traffic in a real industrial environment. We also investigate the impact of various 5G configurations on 5G performance characteristics with insights from the baseband log information as well as unidirectional latency measurements. Our empirical results indicate that 5G mmW system can achieve low latency with high reliability in both one-way traffic directions. The throughput is observed to be high for line-of-sight (LOS) scenarios, making the use of the 5G mmW system appealing especially for data rate-intensive and time-critical industrial use cases. We also observe that industrial environments with lots of metal and reflective surfaces provide favorable propagation conditions for non-LOS transmissions. Our results indicate that static industrial use cases with low mobility can leverage the performance benefits of 5G mmW systems.