The implementation of distributed applications is more frequently achieved through the configuration of service-oriented workflows, which are then deployed within the Edge-Cloud Continuum. This approach facilitates the support of distributed processing pipelines. In this context, there is an increasing demand for solutions that can continuously guarantee the non-functional properties (e.g. security and performance) of such applications. This demand has been boosted by the advent of 5G, where the Continuum is empowered by the ability to involve pervasive 5G Edge Nodes (i.e., Multi-access Edge Computing) and powerful and reliable connectivity links (i.e., network slices). Although capable to support Non-Functional Properties (NFPs) like performance, the current 5G Core Network (CN) is not yet ready to host and execute service workflows nor capable of providing trustworthy guarantees on more advanced NFPs, such as, integrity, security, and robustness. This delay in achieving the full promise of the 5G CN architecture is having a great impact on the capillary diffusion of key technologies such as AI-empowered workflows, which require a fully trusted execution environment to comply with AI regulations such as the AI act. In this paper, we propose an extension of the 5G CN functionalities that supports service workflow deployment and a methodology for the continuous assessment of Non-Functional Properties, beyond simple performance, implemented in a lightweight assurance framework. Our assurance framework is integrated within a 5G simulator to provide a trustworthy 5G CN test-bed and experimentally evaluated in realistic scenarios.