Network Slicing (NS) is an enabling technology to support vertical industries in 5G-and-beyond (B5G) systems. The management of Radio Access Network (RAN) slices re-lies on extensive awareness of network load status and data analysis. With increasingly diversified services and ubiquitous user data, centralized slice management is unsustainable. This paper presents a new distributed load prediction and slicing framework based on Federated Learning (FL). Specifically, we predict the slice-level traffic by designing a Federated Long Short Time Memory (Fed-LSTM) algorithm with a tailored loss function to reduce Service Level Agreement (SLA) violation rate. Given the predicted traffic load, we model slice resource orchestration as an improved two-dimensional Polygon Knapsack (2D- PK) problem, split slice traffic at different granularities, and solve the problem using the Maximal Rectangles Bottom-Left (MAXRECTS-BL) algorithm. Experimental results on real-world captured dataset show that our approach can achieve significant improvement in prediction accuracy, slicing SLA violation and resource utilization, compared to existing techniques.