Network slicing at the edge is becoming a new enabler for 5G and beyond networks to support diverse and differential services, with efficient employment of virtualized resources provided by edge and cloud layers. However, as the arrival patterns of user requests are complicated and unpredictable in practical network scenarios, conventional system architectures and scheduling algorithms for core network slicing cannot handle the uncertain edge user task arrivals properly. Meanwhile, dynamic and intelligent allocation of multi-dimensional resources for edge-aided network slices is also a crucial issue. In this work, we develop a novel intelligent edge-aided network slicing scheme to reduce the system response time. Firstly, a deep belief network (DBN)-based task classification scheme is proposed. Due to the multi-layer structure of DBNs, the nonlinear features of user requests can be extracted efficiently with several individual restricted Boltzmann machines (RBMs). Compared with the classical models for network service classification, the DBNs can avoid over-fitting by the unsupervised pre-training process. Based on the classification results, a resource orchestration (S-RO) algorithm for edge-aided network slicing is investigated to reduce the system response time. Finally, the experiments to evaluate the proposed scheme are conducted with real-world datasets. The experimental results show that the S-RO algorithm is able to improve system throughput for providing network services.