Link Adaptation (LA) in 5G NR relies on channel measurements and HARQ feedback, which quickly become outdated in fast‑varying channels and are noisy, forcing schedulers to choose between overly aggressive or overly conservative rates for predictable performance. Consequently, deployments favor simple, robust algorithms rather than optimal spectral efficiency.\ \ This paper introduces NOSTRAdAMUS, a predictive LA framework that augments existing algorithms without replacing them. It predicts whether a retransmission will occur in the next radio frame from recent HARQ history and applies corrections to the Modulation and Coding Scheme (MCS) chosen by the underlying policy.\ \ Several ML models were benchmarked; Gradient Boosting achieved 82.9% overall accuracy, with high‑confidence interventions correct 94.2% of the time and an inference latency of 5.5 $\mu$s. The model was trained on over‑the‑air (OTA) data collected from the X5G testbed, which uses the open‑source OpenAirInterface (OAI) 5G stack, NVIDIA Aerial, and COTS O‑RAN radios and user equipment. The trained model was deployed as a dApp and evaluated OTA as well as with hardware‑in‑the‑loop channel emulators, covering 3GPP TDL and CDL channels, SISO and MIMO configurations, and pedestrian and vehicular mobility scenarios.\ \ Results show that without retraining, the dApp enhances two state‑of‑the‑art LA algorithms, increasing goodput by up to 71.5% while reducing retransmissions by up to 71.8%. This demonstrates the robustness and generalization capability of the approach.\ \ Review: NOSTRAdAMUS adds a lightweight predictive layer to traditional LA, delivering substantial gains and proving the practicality of machine learning in real‑time wireless resource scheduling.