360° video streaming is a key component of the emerging Virtual Reality (VR) and Augmented Reality (AR) applications. In 360° video streaming, a user may freely navigate through the captured 360° video scene by changing her desired Field-of-View. Highthroughput and low-delay data transfers enabled by 5G wireless networks can potentially facilitate untethered 360° video streaming experience. Meanwhile, the high volatility of 5G wireless links present unprecedented challenges for smooth 360° video streaming. In this paper, novel multi-path multi-tier 360° video streaming solutions are developed to simultaneously address the dynamics in both network bandwidth and user viewing direction. We systematically investigate various design trade-offs on streaming quality and robustness. Through simulations driven by real 5G network bandwidth traces and user viewing direction traces, we demonstrate that the proposed 360° video streaming solutions can achieve a high-level of Quality-of-Experience (QoE) in the challenging 5G wireless network environment.