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To support the diversified 5G usage scenarios, the 5G New Radio (NR) physical layer is enriched with the flexible multi-numerology feature, where multiple frame structures with different sub-carrier spacings coexist in one frequency band. However, this flexibility brings with it a further challenge in Radio Resource Management (RRM), how to best allocate the available band spectrum among the different non-orthogonal numerologies. This work presents a novel Quality of Service (QoS)-aware and channel-aware RRM framework that manages diversified type of services, i.e., Best Effort (BE) services and Guaranteed Bit Rate (GBR) services with different priorities. The goal is to maximize the number of satisfied GBR services, according to the priority, and the throughput of the BE services. To provide a feasible solution, the proposed framework consists of two control levels. The first one appropriately splits the available bandwidth among the various numerologies, with the aim of achieving the above goal, trying to assign continuous portion of band to the same Numerology, in order to mitigate the Inter-Numerology Interference (INI) phenomenon. Moreover, it includes an advanced dropping strategy to support overload conditions. The second level distributes the Physical Resource Blocks (PRBs) to the User Equipments (UEs) belonging to the same numerology, by exploiting scheduling algorithms available in literature. Through an extensive simulation campaign, under different traffic load and channel conditions, we compare the proposed RRM framework with other reference schemes available in literature. The results show that the proposed framework outperforms them in any simulation setup.