Efficient and explainable breast cancer (BC) risk prediction is critical for large-scale population-based screening. Breast MRI provides functional information for personalized risk assessment. Yet effective modeling remains challenging as fully 3D CNNs capture volumetric context at high computational cost, whereas lightweight 2D CNNs fail to model inter-slice continuity. Importantly, breast MRI modeling for shor- and long-term BC risk stratification remains underexplored. In this study, we propose LoGo-MR, a 2.5D local-global structural modeling framework for five-year BC risk prediction. Aligned with clinical interpretation, our framework first employs neighbor-slice encoding to capture subtle local cues linked to short-term risk. It then integrates transformer-enhanced multiple-instance learning (MIL) to model distributed global patterns related to long-term risk and provide interpretable slice importance. We further apply this framework across axial, sagittal, and coronal planes as LoGo3-MR to capture complementary volumetric information. This multi-plane formulation enables voxel-level risk saliency mapping, which may assist radiologists in localizing risk-relevant regions during breast MRI interpretation. Evaluated on a large breast MRI screening cohort (~7.5K), our method outperforms 2D/3D baselines and existing SOTA MIL methods, achieving AUCs of 0.77-0.69 for 1- to 5-year prediction and improving C-index by ~6% over 3D CNNs. LoGo3-MR further improves overall performance with interpretable localization across three planes, and validation across seven backbones shows consistent gains. These results highlight the clinical potential of efficient MRI-based BC risk stratification for large-scale screening. Code will be released publicly.