With the rapid development of 5G networks, the emerging 5G mobile system is expected to serve a large number of users with differentiated performance requirements. Different application scenarios have differentiated resource and quality of service requirements. To optimize the allocation of network multidimensional resources, an allocation algorithm to maximize multi-dimensional resource utilization is proposed for the resource optimization problem of Enhanced Mobile Broadband (eMBB) and Ultra-Reliable and Low Latency Communication (URLLC) network slices. The algorithm combines communication, computing and storage resources to provide a solution for multi-dimensional resource allocation. And it is able to guarantee the high speed demand of users in eMBB slices and the low latency demand of users in URLLC slices. The resource problem for multiservice slicing is modelled as a non-linear mixed integer programming problem. Combining the augmented Lagrange algorithm and the branch-and-bound method to solve the problem, the optimal resource allocation strategy is obtained. It is demonstrated that the proposed algorithm can improve the system throughput, increase the resource utilization, improve the rate of eMBB class services and reduce the delay of URLLC class services compared with other algorithms.