Mobility Management in 5G is challenging due to the usage of high frequencies and dense cell deployments. This often results in frequent handovers for users, causing disruptions in transmission and reception and adversely affecting network capacity. The crucial task is to integrate handover decisions with resource allocation, ensuring the target base station guarantees the minimum required user rate while optimizing metrics that are essential for the operator, such as network sum throughput. The dynamic allocation of resources to BSs, facilitated by Software-Defined Radio Access Network (SD-RAN), emerges as a solution for efficient resource utilization. This paper aims to maximize network sum throughput, ensure a minimum user rate, and minimize handovers. We adopt a two-level approach, integrating resource allocation and mobility management using SD-RAN. This is modeled as an integer nonlinear program, and by relaxing it, we obtain an upper bound. Given the NP-hard nature of the problem, we introduce two heuristics (deterministic and probabilistic) which yield near-optimal user-to-BS assignments and efficiently allocate resources to serving BSs and end users. Our proposed algorithms outperform state of the art, significantly reducing the handover rate while remaining within 2% of the optimum, with user rate satisfaction reaching 99%.