Recent developments in the aerospace industry have led to a dramatic reduction in the manufacturing and launch costs of low Earth orbit satellites. The new trend enables the paradigm shift of satellite-terrestrial integrated networks with global coverage. In particular, the integration of 5G communication systems and satellites has the potential to restructure next-generation mobile networks. By leveraging the network function visualization and network slicing, the satellite 5G core networks will facilitate the coordination and management of network functions in satellite-terrestrial integrated networks. We are the first to deploy a 5G core network on a real-world satellite to investigate its feasibility. We conducted experiments to validate the satellite 5G core network functions. The validated procedures include registration and session setup procedures. The results show that the satellite 5G core network can function normally and generate correct signaling.