Deep learning (DL) techniques are gaining more and more attention in the software engineering community. They have been used to support several code-related tasks, such as automatic bug fixing and code comments generation. Recent studies in the Natural Language Processing (NLP) field have shown that the Text-To-Text Transfer Transformer (T5) architecture can achieve state-of-the-art performance for a variety of NLP tasks. The basic idea behind T5 is to first pre-train a model on a large and generic dataset using a self-supervised task ( e.g: filling masked words in sentences). Once the model is pre-trained, it is fine-tuned on smaller and specialized datasets, each one related to a specific task ( e.g: language translation, sentence classification). In this paper, we empirically investigate how the T5 model performs when pre-trained and fine-tuned to support code-related tasks. We pre-train a T5 model on a dataset composed of natural language English text and source code. Then, we fine-tune such a model by reusing datasets used in four previous works that used DL techniques to: (i) fix bugs, (ii) inject code mutants, (iii) generate assert statements, and (iv) generate code comments. We compared the performance of this single model with the results reported in the four original papers proposing DL-based solutions for those four tasks. We show that our T5 model, exploiting additional data for the self-supervised pre-training phase, can achieve performance improvements over the four baselines.