The accurate prediction of required resources in terms of storage, computing and bandwidth is essential for 5G to host diverse services. The existing efforts illustrate that it is more promising to efficiently predict the unknown required resources with a third-order tensor compared to the 2D-matrix-based solutions. However, most of them fail to leverage the inherent features hidden in network traffic like temporal stability and service correlation to build a third-order tensor for the multi-dimensional required resource prediction in an intelligent manner, incurring coarse-grained prediction accuracy. Furthermore, it is difficult to build a third-order tensor with rate-varied measurements in 5G due to different lengths of measurement time slots. To address these issues, we propose an Accurate Prediction of Multi-Dimensional Required Resources (APMR) approach in 5G via Federated Deep Reinforcement Learning (FDRL). We first confirm the resource requests originated from different Base Stations (BSs) at varied measurement rates have similar features in service and time domains, but cannot directly form a series of regular tensors. Built on these observations, we reshape these measurement data to form a series of standard third-order tensors with the same size, which include many elements obtained from measurements and some unknown elements needed to be inferred. In order to obtain accurately predicted results, the FDRL-based tensor factorization approach is introduced to intelligently utilize multiple specific iteration rules for local model learning, and the accuracy-aware and latency-based depreciation strategies are exploited to aggregate local models for resource prediction. Extensive simulation experiments demonstrate that APMR can accurately predict the multi-dimensional required resources compared to the state-of-the-art approaches.