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Along with the increasing demand for latencysensitive services and applications, Deterministic Network (DetNet) concept has been recently proposed to investigate deterministic latency assurance for services featured with bounded latency requirements in 5G edge networks. The Network Function Virtualization (NFV) technology enables Internet Service Providers (ISPs) to flexibly place Virtual Network Functions (VNFs) achieving performance and cost benefits. Then, Service Function Chains (SFC) are formed by steering traffic through a series of VNF instances in a predefined order. Moreover, the required network resources and placement of VNF instances along SFC should be optimized to meet the deterministic latency requirements. Therefore, it is significant for ISPs to determine an optimal SFC deployment strategy to ensure network performance while improving the network revenue. In this paper, we jointly investigate the resource allocation and SFC placement in 5G edge networks for deterministic latency assurance. We formulate this problem as a mathematic programming model with the objective of maximizing the overall network profit for ISP. Furthermore, a novel Deterministic SFC deployment (Det-SFCD) algorithm is proposed to efficiently embed SFC requests with deterministic latency assurance. The performance evaluation results show that the proposed algorithm can provide better performance in terms of SFC request acceptance rate, network cost reduction, and network resource efficiency compared with benchmark strategy.