Chinese national pentatonic modes, with five tones of Gong, Shang, Jue, Zhi and Yu as the core, play an essential role in traditional Chinese music culture. After the early twentieth century, with the development of new Chinese music, the ancient Chinese theory of scales gradually developed into a new pentatonic modes theory under the influence of western music. In this paper, we briefly introduce our self-built CNPM (Chinese National Pentatonic Modes) Dataset, then design residual convolutional neural network models to identify which TongGong system the mode belongs, the pitch of tonic, the mode pattern and the mode type from audio signals, in combination with musical domain knowledge. We use both single-task and multi-task models with three strategies for identification, and compare them with a simple template-based baseline method. In experiments, we use seven accuracy metrics to evaluate the models. The results on identifying both the tonic pitch and the pattern of mode correctly achieve an average accuracy of 69.65%. As an initial research on automatic Chinese national pentatonic modes recognition, this work will contribute to the development of multicultural music information retrieval, computational ethnomusicology and five-tone music therapy.