5G-and-beyond mobile communication systems can benefit from Virtualized Network Functions (VNFs) when deployed on cloud infrastructures to achieve elasticity and scalability to provide novel services, such as massive MTC for IoT use cases. 3GPP has developed a transition from point-to-point architecture between network entities to service-based architecture. However, new challenges arise regarding managing Network Functions (NFs) states. Especially control plane VNFs, mainly found in cellular core networks like the 5G Core (5GC), received little attention since the shift towards virtualizing NFs. Most existing solutions for these core networks are often complex and intrusive and must comply more with the standard. These devices communicate more deterministically, bringing new opportunities for elaborated state management. This work presents a feasibility study for measurements of state access patterns rigorously. Measurement results provide a solid base for designing an efficient, lightweight state management service toward realizing stateless design for 5G Core's network functions.