The grand objective of 5G wireless technology is to support three generic services with vastly heterogeneous requirements: enhanced mobile broadband (eMBB), massive machine-type communications (mMTC), and ultra-reliable low-latency communications (URLLC). Service heterogeneity can be accommodated by network slicing, through which each service is allocated resources to provide performance guarantees and isolation from the other services. Slicing of the Radio Access Network (RAN) is typically done by means of orthogonal resource allocation among the services. This work studies the potential advantages of allowing for non-orthogonal sharing of RAN resources in uplink communications from a set of eMBB, mMTC and URLLC devices to a common base station. The approach is referred to as Heterogeneous Non-Orthogonal Multiple Access (H-NOMA), in contrast to the conventional NOMA techniques that involve users with homogeneous requirements and hence can be investigated through a standard multiple access channel. The study devises a communication-theoretic model that accounts for the heterogeneous requirements and characteristics of the three services. The concept of reliability diversity is introduced as a design principle that leverages the different reliability requirements across the services in order to ensure performance guarantees with non-orthogonal RAN slicing. This study reveals that H-NOMA can lead, in some regimes, to significant gains in terms of performance trade-offs among the three generic services as compared to orthogonal slicing.