With the burgeon deployment of the fifth-generation new radio (5 G NR) networks, the codebook plays a crucial role in enabling the base station (BS) to acquire the channel state information (CSI). Different 5 G NR codebooks incur varying overheads and exhibit performance disparities under diverse channel conditions, necessitating codebook adaptation based on channel conditions to reduce feedback overhead while enhancing performance. However, existing methods of 5 G NR codebooks adaptation require significant overhead for model training and feedback or fall short in performance. To address these limitations, this letter introduces a federated reservoir computing framework designed for efficient codebook adaptation in computationally and feedback resource-constrained mobile devices. This framework utilizes a novel series of indicators as input training data, striking an effective balance between performance and feedback overhead. Compared to conventional models, the proposed codebook adaptation via federated reservoir computing (CA-FedRC), achieves rapid convergence and significant loss reduction in both speed and accuracy. Extensive simulations under various channel conditions demonstrate that our algorithm not only reduces resource consumption of users but also accurately identifies channel types, thereby optimizing the trade-off between spectrum efficiency, computational complexity, and feedback overhead.