Deep learning has been widely used recently for sound event detection and classification. Its success is linked to the availability of sufficiently large datasets, possibly with corresponding annotations when supervised learning is considered. In bioacoustic applications, most tasks come with few labelled training data, because annotating long recordings is time consuming and costly. Therefore supervised learning is not the best suited approach to solve bioacoustic tasks. The bioacoustic community recasted the problem of sound event detection within the framework of few-shot learning, i.e. training a system with only few labeled examples. The few-shot bioacoustic sound event detection task in the DCASE challenge focuses on detecting events in long audio recordings given only five annotated examples for each class of interest. In this paper, we show that learning a rich feature extractor from scratch can be achieved by leveraging data augmentation using a supervised contrastive learning framework. We highlight the ability of this framework to transfer well for five-shot event detection on previously unseen classes in the training data. We obtain an F-score of 63.46\% on the validation set and 42.7\% on the test set, ranking second in the DCASE challenge. We provide an ablation study for the critical choices of data augmentation techniques as well as for the learning strategy applied on the training set.