The 5G core network will employ network slices, logical networks over physical infrastructure, each of which provides a specific service. There are two typical methods for network slicing: the hop- by-hop method using SDN and the edge-overlay method using Layer 2 over Layer 3 (L2 over L3) tunneling. In the hop-by-hop method, migration from the existing infrastructure is difficult and the SDN controller will become a single point of failure. In the edge-overlay method, tunneling causes header overhead and throughput degradation. This paper proposes a network slicing method without using SDN nor tunneling for the 5G core network using IPv6. In the proposed method, the lower 64-bit part of an IPv6 address (the node identifier) identifies a node and the upper 64-bit part (the locator) specifies the subnet to which the node is attached. This approach is suitable to support mobility management without tunneling such as MocLis. The slice identifier and the subnet number in the slice are embedded within the locator. Thus, the proposed method avoids the problems of system migration, a single point of failure, header overhead, and throughput degradation. In the proof of concept prototype, a Docker container is used as a virtual node in a network slice and a MPLS label-switched path is used as a virtual link between virtual nodes. TCP Throughput evaluation shows that the proposed method is superior to the edge-overlay method.