Service Function Chaining (SFC) is a key enabler for network slicing in the Fifth-Generation (5G) mobile networks. Despite the ongoing standardisation activities and open source projects in addressing SFC, built-in 5G network support for SFC has not been sufficiently addressed on 5G Multi-tenant infrastructures. This paper proposes an Service Function Forwarder (SFF) and Classifier which is able to provide network slicing capabilities to the Service Data Plane in this type of infrastructures. The proposed prototype has been implemented as an extension of the popular Open Virtual Switch (OVS). The results of the empirical validation demonstrate that the proposed prototype is able to deal simultaneously with up to 8192 network slices with a maximum delay of 11 microseconds and 0% packet loss processing traffic at speeds up to 20 Gbps in a 5G architecture. The performance values achieved in this work are compliant with the 5G KPI expectation.