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The Third-Generation Partnership Project (3GPP) has identified network slicing as one of the key technologies to address the complex communication scenarios in the 5G network. With the 5G commercialization target dates fast approaching, there are a plethora of challenges that need to be addressed regarding 5G slicing especially in the Radio Access Network (RAN). Consequently, this paper highlights the key research challenges being addressed by the Ph. D. thesis proposal. Specifically, we propose a virtualized RAN slicing framework considering a multi-RAT, multi-domain heterogeneous network and a two-level resource allocation scheme at each domain. Within a slice, we adopt a novel concept of slice profiles to address the heterogeneity challenges associated with the 3GPP notion of a slice. We also propose an entity called cross-domain coordinator to coordinate inter-domain resource sharing. The paper discusses the approaches to be adopted in formulating the intra-domain and inter-domain resource sharing algorithms.