Network slicing, where a single physical network is partitioned into several fit-for-purpose virtual networks with different degrees of isolation and quality of service (QoS), is a key enabler of 5G and beyond mobile networks. However, it is prone to security threats such as Distributed Denial-of-Service (DDoS) attacks. In this paper, we propose a solution based on Deep Learning (DL) that detects such attacks, and then creates a sinkhole-type slice with a small portion of physical resources to isolate and mitigate the attackers' action. Using our 5G prototype based on OpenAirInterface, we evaluate our approach by comparing several DL models in terms of detection accuracy, false positive rate, execution time, among other Machine Learning-related metrics. We also assess the performance of created 5G network slices in terms of benign/malicious users' throughput, as well as the processing time during the slicing operations. Results show that our approach is able to detect DDoS attacks in a timely manner with an accuracy of almost 97% and a false positive rate of less than 4%. We also show that our approach decreases the network throughput for the malicious users by a factor of 15, while maintaining a high network throughput for benign users.