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The core network architecture of telecommunication systems has undergone a paradigm shift in the fifth-generation (5G) networks. 5G networks have transitioned to software-defined infrastructures, thereby reducing their dependence on hardware-based network functions. New technologies, like network function virtualization and software-defined networking, have been incorporated in the 5G core network (5GCN) architecture to enable this transition. This has resulted in significant improvements in efficiency, performance, and robustness of the networks. However, this has also made the core network more vulnerable, as software systems are generally easier to compromise than hardware systems. In this article, we present a comprehensive security analysis framework for the 5GCN. The novelty of this approach lies in the creation and analysis of attack graphs of the software-defined and virtualized 5GCN through machine learning. This analysis points to 119 novel possible exploits in the 5GCN. We demonstrate that these possible exploits of 5GCN vulnerabilities generate five novel attacks on the 5G Authentication and Key Agreement protocol. We combine the attacks at the network, protocol, and the application layers to generate complex attack vectors. In a case study, we use these attack vectors to find four novel security loopholes in WhatsApp running on a 5G network.