As network slicing is an enabling technology for the fifth-generation (5G) networks, it comes with complex challenges to ensure that resource management is consistent with slice tenant activities to provide better performance and cost-effective services to different tenants tailored to their needs. To this end, traffic classification is fundamental for the provisioning of the resources in a network by analyzing the network traffic to anticipate future requests. However, the massive increase of heterogeneous traffic features challenges dynamic network slices traffic classification. Previous literature have explored statistical and machine learning techniques but are constrained by feature engineering and computational costs. In this letter, we propose the multi-lane CapsNet assisted network traffic classification (MANTA), a framework based on multi-lane Capsule Networks (CapsNet) deep learning technique, to identify and classify heterogeneous traffic flows in 5G network slicing. Furthermore, we conduct a comparative analysis of the model with previous literature using deep learning techniques. The experimental results exhibit improved performance with high accuracy of 97.3975%, compared with other classifiers from previous literature.