As over-the-top (OTT) applications such as videos dominate the global mobile traffic, conventional content delivery techniques such as caching no longer suffice to cope with mobile network users' requirements due to e.g., fluctuating radio conditions. In legacy 4G networks, mobile network operator (MNO) and OTT service providers (OSPs) are logically decoupled from each other, hence preventing them to share necessary context and enable in-network context-aware intelligence. The recently standardized 5G network architecture's softwarized and virtualized nature opens up new opportunities for flexible deployment of MNO- and OSP-operated network functions. In this work, we first extend the current 5G standard to enable third-party stakeholders to deploy their own user-plane functions (UPFs) within the MNO infrastructure. Based on this, we propose a service function chaining (SFC) framework within the 5G core network, which allows MNO to dynamically determine the optimal set of UPFs that each flow should traverse based on their real-time contexts. The proposed framework has been implemented in a testbed network. Through realistic experiments, we demonstrate that UPF deployment strategy plays a crucial rule in the resulting SFC performance, and our proposed scheme can achieve performance that is close to the benchmark. Furthermore, we establish recommendations on best practices of UPF deployment strategies in 5G network.