With the rapid advancement of 5G network technology, cyber security threats are intensifying. The fifth-generation mobile communication for railways (5G-R), as a product of the deep integration of the railway industry with 5G technology, plays a crucial role in ensuring the operational safety of railways. Cyber security assessment is one of the key components in safeguarding network security, and attack graphs are one of the mainstream models for cyber security assessment methods. This paper focuses on optimizing the method for assessing the security of the 5G-R core network based on attack graphs. By integrating the business security requirements of the 5G-R core network, this paper optimizes the parameters for the conventional vulnerability assessment methods and the influencing indicators of atomic attack success probability. It also constructs a formula for calculating the atomic attack success probability based on the fuzzy analytic hierarchy process (AHP). By setting up a simulated environment of the 5G-R core network within a network target field, this paper conducts the feasibility verification of the assessment method for 5G-R core cyber security. Comparative experiments with the conventional common vulnerability scoring system (CVSS) and methods used in existing literature prove the validity and superiority of the proposed model.