It is clear that 5G networks have already become integral to our present. However, a significant issue lies in the fact that current 5G communication systems are incapable of fully ensuring the required quality of service and the security of transmitted data, especially in government networks that operate in the context of the Internet of Things, hostilities, hybrid warfare, and cyberwarfare. The use of 5G extends to critical infrastructure operators and special users such as law enforcement, governments, and the military. Adapting modern cellular networks to meet the specific needs of these special users is not only feasible but also necessary. In doing so, these networks must meet additional stringent requirements for reliability, performance, and, most importantly, data security. This scientific paper is dedicated to addressing the challenges associated with ensuring cybersecurity in this context. To effectively improve or ensure a sufficient level of cybersecurity, it is essential to measure the primary indicators of the effectiveness of the security system. At the moment, there are no comprehensive lists of these key indicators that require priority monitoring. Therefore, this article first analyzed the existing similar indicators and presented a list of them, which will make it possible to continuously monitor the state of cybersecurity systems of 5G cellular networks with the aim of using them for groups of special users. Based on this list of cybersecurity KPIs, as a result, this article presents a model to identify and evaluate these indicators. To develop this model, we comprehensively analyzed potential groups of performance indicators, selected the most relevant ones, and introduced a mathematical framework for their quantitative assessment. Furthermore, as part of our research efforts, we proposed enhancements to the core of the 4G/5G network. These enhancements enable data collection and statistical analysis through specialized sensors and existing servers, contributing to improved cybersecurity within these networks. Thus, the approach proposed in the article opens up an opportunity for continuous monitoring and, accordingly, improving the performance indicators of cybersecurity systems, which in turn makes it possible to use them for the maintenance of critical infrastructure and other users whose service presents increased requirements for cybersecurity systems.