Cloud computing is being embraced more and more by telecommunication operators for on-demand access to computing resources. Knowing that 5G Core reference architecture is envisioned to be cloud-native and service-oriented, we propose, in this paper, offloading to the cloud, some of 5G delay-tolerant Network Functions and in particular the Network Data Analytics Function (NWDAF). The dynamic selection of cloud resources to serve off-loaded 5G-NWDAF, while incurring minimum cost and maximizing utilization of served next generation Node-Bs (gNBs) requires agility and automation. This paper introduces a framework to automate the selection process that satisfies resource demands while meeting two objectives, namely, cost minimization and utilization maximization. We first formulate the mapping of gNBs to 5G-NWDAF problem as an Integer Linear Program (ILP). Then, we propose a heuristic to solve it based on branch-cut-and-price technique combining all of branch-andprice, branch-and-cut and branch-and-bound. Results using pricing data from a public cloud provider (Google Cloud Platform), show that our proposal achieves important savings in cloud computing costs and reduction in execution time compared to other state-of-the-art frameworks.