The network function virtualization (NFV) enables the virtual network functions (VNFs) to run as software components upon a virtualization system hosted in a cloud. Recently, due to its high flexibility and elasticity in terms of network services and functions deploying, NFV has been considered as one of the key enabling techniques of the fifth-generation (5G) wireless systems. Moreover, the creation of the core network functions is the key to the implementation of 5G. Currently, there are extensive studies researching into how to deploy cooperatively VNFs over a federated cloud for multiple cloud providers (CPs) to create the 5G Core. These studies have a critical assumption that each CP participating in the cooperation is fully informed of all the information about other CPs. However, the assumption may not hold in practice. Since CPs adopt diverse virtualization technologies (e.g., XEN, KVM, or containers), the cost to create an instance of one VNF for each CP may be different. Moreover, the cost information is private and will not be shared with each other. Consequently, it is difficult for each CP to determine whether to cooperate with others and the way of cooperation. Therefore, in this paper, we utilize the Bayesian coalition formation game (BCFG) to tackle this challenging situation with the unknown information about CPs and formulate the optimal coalition that can deploy cooperatively each VNFs of 5G Core. Specifically, we address the optimal number of VNF instances to instantiate, the number of virtual resources for each instance, and the placement decision in a specific CP over a federated cloud. We propose a BCFG-based non-myopic and full negotiation approach for the creation of the virtual 5G Core network functions. Simulation results demonstrate the comprehensive performance of the proposed method in terms of convergence properties and the profits that each participating CP can obtain.