The 5G telecommunication ecosystem is expected to dynamically support new and various applications from the industrial and the service sectors that are very heterogeneous in terms of QoS and resources’ requirements. In this context, a promising important concept for network resource management is emerging, denoted by Network Slicing. It involves decisions on embedding and managing several virtual networks on the same physical resources. This problem in its simplified form can be modeled by the Virtual Network Embedding (VNE) problem. In this paper, we propose a new resolution method, in which we first reduce the set of admitted routes and then solve an integer program. Our proposed approach is then compared to the optimal solution and to a method from the state of the art. Obtained results show that our approach provides good result in terms of slice acceptance ratio and resource consumption while reducing the overall complexity and runtime.