The 5th generation mobile network (5G) is designed with a new core architecture that makes it quite extensible. The components of the 5G core architecture are no longer physical standalone devices, but rather software processes run on commercial off-the-shelf (COTS) servers. The backbone of 5G is software-defined networking (SDN) and network function virtualization (NFV), and they both bring unprecedented flexibility to network and resource management. In this context, 5G logical networks can be created by partitioning a shared physical infrastructure, and each network can be customized and optimized for specific entity. This concept is known as 5G network slicing. Despite the tremendous benefits of network slicing, it also brings many unprecedented security challenges because of the dynamism and diversity of slice's structure. Therefore, establishing trust in the 5G ecosystem is a cornerstone for global adaptation and tackling security and privacy risks. In this paper, we focus on the trust aspect between the network slice stakeholders (i.e slice owners, users, slice resource providers, and service providers), and we propose a blockchain-based zero trust model that addresses threat models that are based on the lack of trust between the entities in a network slice. Our approach for zero trust modeling and quantification is based on direct evidence and indirect evidence and the use of smart contracts with blockchain to maintain the required trust values at runtime. We provide details on how to model and quantify the trust of all the stakeholders of a given network slice and how the blockchain smart contract can enforce the zero-trust requirements for all network slice stakeholders.