The classical theory of control systems focused mainly on control objects, which are characterized by a certain determinism, stationarity, relative simplicity, fixity of coordinates, sufficiently studied characteristics, and the possibility of building regular mathematical models. These characteristics were fully met by telecommunication networks with channel switching, including mathematical network models for calculating resources by means of mass service theory. Over time, new problems arise that require new solutions and, accordingly, new approaches to managing information communications, which is considered in this study. The research analyzed trends in the construction of fifth generation 5G networks. The relevance of the study of new approaches to the management of information communications is shown. The main stages of the evolution of telecommunications as an object of management are indicated. Problems corresponding to this evolution and approaches to their solution are outlined. Forecasts of the development and complications of telecommunications in the 2020s and 2030s are offered. Self-organization and multi-agent systems are considered within the framework of the analysis of telecommunications management as a scientific discipline. The concept of the correctness of the management strategy at certain moments of time and always, that is, at all moments of time of the considered period, is formalized. A new probabilistic-parametric concept of three-level management of 5G information and communication networks is substantiated. Approaches to mathematical modeling of telecommunications management within the framework of this concept are proposed. The relevance of the development of new methods for calculating probabilistic-temporal characteristics of management of fifth generation communication networks in real time has been proven. Ways to develop research on software-configured networks and virtualization of the functionality of post-NGN networks are proposed.