For the voice services under 5G, the prediction of the IMS signaling storm is the foundation for ensuring the stable operation of Voice over New Radio (VoNR) services and strengthening the intelligent management of 5G networks. Simultaneously, it is also an important approach for operators to enhance their core competitiveness. However, the IP Multimedia Subsystem (IMS) signaling storm prediction alarm function for live network systems is still not robust, with most attention being directed towards equipment fault detection and network element health monitoring. Given this limitation of the live network management system, a method combining 2 modules of prediction and judgment is proposed in this research to realize a more advanced prediction of IMS signaling storms. Among this proposed method, a new neurally network model named Trigonometric Particle Swarm Ptimization-Long Short Term Memory-Attention Mechanism (TRIGPSO-LSTM-AM) is constructed and served as the cornerstone of the method. Firstly, the LSTM-AM model, which combines temporal recurrent neural networks with attention mechanism, is established to predict the key index values of the IMS. At the same time, the traditional Particle Swarm Optimization (PSO) algorithm is improved, and a more intelligent particle swarm optimization algorithm based on trigonometric transformation, named TRIGPSO, is proposed to enhance the convergence of the prediction model. Then, an alarm judgment module is built, and the output of the prediction module is utilized as the input for this module. Clustering is achieved based on the KMeans algorithm, and each class is mapped to the alarm level, thereby informing the network management to execute the corresponding alarm operation. Finally, the effectiveness and rationality of the proposed method are validated through several groups of comparative experiments.