5G cellular networks are envisioned to support a wide range of emerging delay-oriented services with different delay requirements (e.g., 20ms for VR/AR, 40ms for cloud gaming, and 100ms for immersive video streaming). However, due to the highly variable and unpredictable nature of 5G access links, existing end-to-end (e2e) congestion control (CC) schemes perform poorly for them. In this paper, we demonstrate that properly blending non-deterministic exploration techniques with straightforward proactive and reactive measures is sufficient to design a simple yet effective e2e CC scheme for 5G networks that can: (1) achieve high controllable performance, and (2) possess provable properties. To that end, we designed Reminis and through extensive experiments on emulated and real-world 5G networks, show the performance benefits of it compared with different CC schemes. For instance, averaged over 60 different 5G cellular links on the Standalone (SA) scenarios, compared with a recent design by Google (BBR2), Reminis can achieve 2.2x lower 95th percentile delay while having the same link utilization.