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Trust, security, and privacy are three of the major pillars to assemble the fifth generation network and beyond. Despite such pillars are principally interconnected, they arise a multitude of challenges to be addressed separately. 5G ought to offer flexible and pervasive computing capabilities across multiple domains according to user demands and assuring trustworthy network providers. Distributed marketplaces expect to boost the trading of heterogeneous resources so as to enable the establishment of pervasive service chains between cross-domains. Nevertheless, the need for reliable parties as ``marketplace operators'' plays a pivotal role to achieving a trustworthy ecosystem. One of the principal blockages in managing foreseeable networks is the need of adapting previous trust models to accomplish the new network and business requirements. In this regard, this article is centered on trust management of 5G multi-party networks. The design of a reputation-based trust framework is proposed as a Trust-as-a-Service (TaaS) solution for any distributed multi-stakeholder environment where zero trust and zero-touch principles should be met. Besides, a literature review is also conducted to recognize the network and business requirements currently envisaged. Finally, the validation of the proposed trust framework is performed in a real research environment, the 5GBarcelona testbed, leveraging 12% of a 2.1GHz CPU with 20 cores and 2% of the 30GiB memory. In this regard, these outcomes reveal the feasibility of the TaaS solution in the context of determining reliable network operators.