Network Slicing (NS) is recognized as a key technology for the 5G network in providing tailored network services towards various types of verticals over a shared physical infrastructure. It offers the flexibility of on-demand provisioning of diverse services based on tenants' requirements in a dynamic environment. In this work, we focus on two important issues related to 5G Core slices: the deployment and the reconfiguration of 5G Core NSs. Firstly, for slice deployment, balancing the workloads of the underlying network is beneficial in mitigating resource fragmentation for accommodating the future unknown network slice requests. In this vein, we formulate a load-balancing oriented 5G Core NS deployment problem through an Integer Linear Program (ILP) formulation. Further, for slice reconfiguration, we propose a reactive strategy to accommodate a rejected NS request by reorganizing the already-deployed NSs. Typically, the NS deployment algorithm is reutilized with slacked physical resources to find out the congested part of the network, due to which the NS is rejected. Then, these congested physical nodes and links are reconfigured by migrating virtual network functions and virtual links, to re-balance the utilization of the whole physical network. To evaluate the performance of deployment and reconfiguration algorithms we proposed, extensive simulations have been conducted. The results show that our deployment algorithm performs better in resource balancing, hence achieves higher acceptance ratio by comparing to existing works. Moreover, our reconfiguration algorithm improves resource utilization by accommodating more NSs in a dynamic environment.