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Network Functions Virtualization (NFV) allows flexibility, scalability, agility, and easy manageability of networks by leveraging the features of virtualization and cloud computing technologies. However, softwarization of network functions imposes many challenges. Reliability and latency are major challenges in NFV-enabled 5G networks that can lead to customer dissatisfaction and revenue loss. In general, redundancy is used to improve the reliability of communication services. However, redundancy requires the same amount of additional resources and thus increases cost. In this work, we address the reliability-aware, delay guaranteed, and resource efficient Service Function Chain (SFC) placement problem in softwarized 5G networks. First, we propose a novel SFC subchaining method to enhance the reliability of an SFC without backups. If reliability requirement is not met after subchaining method, we add backups to VNFs to meet the reliability requirement. Then, we formulate the reliable SFC placement problem as an Integer Linear Programming (ILP) problem in order to solve it optimally. Owing to high computational complexity of the ILP problem for solving large input instances, we propose a modified stable matching algorithm to provide near-optimal solution in polynomial time. By extensive simulations we show that our proposed solutions consume lesser physical resources compared to state-of-the-art solutions for provisioning reliable communication services.