This research turn over comprehensively into the transformative realm of 5G network slicing, an innovative paradigm facilitating the creation of virtualized and isolated network instances tailored to diverse service requirements. With a primary focus on securing the slicing mechanism within the dynamic 5G ecosystem, the study meticulously analyses various mitigation techniques, emphasizing the effectiveness of Secure Key Management (SKM) and its intricate mathematical foundations. The intricate nature of 5G network slicing demands a thorough investigation into potential vulnerabilities, extending beyond surface-level scrutiny to address inter and intra-slice security concerns. Recognizing security as a nuanced challenge, the study explores the adaptability and efficacy of SKM in fortifying security and ensuring confidentiality within network slices. By bridging theoretical understanding with practical insights, the research derives fundamental mathematical equations that contribute to academic discourse and offer tangible guidance for real-world implementation. Findings illuminate SKM's efficacy as a robust security measure, particularly in addressing vulnerabilities which can be exploited inter-slice and intra-slice threats. The derived mathematical equations solidify the theoretical foundation of SKM while providing a roadmap for practical application. In the realm of 5G, where Secure Network Slicing is increasingly vital, researchers contribute in-depth insights into challenges and threats, emphasizing the need for robust security mechanisms throughout the lifecycle of network slices. Vulnerabilities are identified on two fronts, inter-slice and intra-slice, prompting the proposal of concrete solutions, with SKM as a critical player.