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Network slicing has been considered as one of the key enablers for 5G to support diversified services and application scenarios. This paper studies the distributed network slicing utilizing both the spectrum resource offered by communication network and computational resources of a coexisting fog computing network. We propose a novel distributed framework based on a new control plane entity, regional orchestrator (RO), which can be deployed between base stations (BSs) and fog nodes to coordinate and control their bandwidth and computational resources. We propose a distributed resource allocation algorithm based on Alternating Direction Method of Multipliers with Partial Variable Splitting (DistADMM-PVS). We prove that the proposed algorithm can minimize the average latency of the entire network and at the same time guarantee satisfactory latency performance for every supported type of service. Simulation results show that the proposed algorithm converges much faster than some other existing algorithms. The joint network slicing with both bandwidth and computational resources can offer around 15% overall latency reduction compared to network slicing with only a single resource.