Cellular communication technologies such as 5G are deployed on a large scale around the world. Compared to other communication technologies such as WiFi, Bluetooth, or Ultra Wideband, the 5G communication standard describes support for a large variety of use cases, e.g., Internet of Things, vehicular, industrial, and campus-wide communications. An organization can operate a Private 5G network to provide connectivity to devices in their manufacturing environment. Physical Layer Key Generation (PLKG) is a method to generate a symmetric secret on two nodes despite the presence of a potential passive eavesdropper. To the best of our knowledge, this work is one of the first to implement PLKG in a real Private 5G network. Therefore, it highlights the possibility of integrating PLKG in the communication technology highly relevant for industrial applications. This paper exemplifies the establishment of a long-term symmetric key between an aerial vehicle and IT infrastructure both located in a manufacturing environment and communicating via the radio interface of the Private 5G network.