5G network slicing is a fundamental technology for concurrent delivery of 5G services and is key for a service-driven evolution that can meet unprecedented SLAs deterministically across end-to-end network resources. This paper focuses on the application of network slicing in the transport domain and explains how its concepts fit in the 3GPP 5G architecture, including transport slicing (also known as transport sub-slicing). It describes the benefits of slicing in maximizing operational flexibility and efficiency. It introduces the concept of a transport slice controller for automating transport network slice creation, optimization and assurance in supporting a large range of 5G deployment scenarios, including 4G/5G hybrids leveraging existing network investments.