One of the requirement of 5G is to support massive number of connected devices, considering many use-cases such as IoT and massive Machine Type Communication (MTC). While this represents an interesting opportunity for operators to grow their business, it will need new mechanisms to scale and manage the envisioned high number of devices and their generated traffic. Particularity, the signaling traffic, which will overload the 5G core Network Function (NF) in charge of authentication and mobility, namely Access and Mobility Management Function (AMF). The objective of this paper is to provide an algorithm based on Control Theory allowing: (i) to equilibrate the load on the AMF instances in order to maintain an optimal response time with limited computing latency; (ii) to scale out or in the AMF instance (using NFV techniques) depending on the network load to save energy and avoid wasting resources. Obtained results via computer system indicate the superiority of our algorithm in ensuring fair load balancing while scaling dynamically with the traffic load.