Unmanned aerial vehicles (UAVs) and communication systems are fundamental elements in Mission Critical services, such as search and rescue. In this article, we introduce an architecture for managing and orchestrating 5G and beyond networks that operate over a heterogeneous infrastructure with UAVs' aid. UAVs are used for collecting and processing data, as well as improving communications. The proposed System Intelligence (SI) architecture was designed to comply with recent standardization works, especially the ETSI Experiential Networked Intelligence specifications. Another contribution of this article is an evaluation using a testbed based on a virtualized non-standalone 5G core and a 4G Radio Access Network (RAN) implemented with open-source software. The experimental results indicate, for instance, that SI can substantially improve the latency of UAV-based services by splitting deep neural networks between UAV and edge or cloud equipment. Other experiments explore the slicing of RAN resources and efficient placement of virtual network functions to assess the benefits of incorporating intelligence in UAV-based mission-critical services.