This proceedings volume collects contributions from the 5th AIRO Young Workshop and AIRO PhD School 2021 joint event on "Optimization and Data Science: Trends and Applications", held online, from February 8 to 12, 2021. The joint event was organized by AIROYoung representatives and the Operations Research Group of the Department of Electrical Engineering and Information Technology of the University "Federico II" of Naples. The selected contributions represent the state-of-the-art knowledge related to different branches of research, such as data science, machine learning and combinatorial optimization. Therefore, this book is primarily addressed to researchers and PhD students of the operations research community. However, due to its interdisciplinary content, it will be of high interest for other closely related research communities. Moreover, this volume not only presents theoretical results but also covers real applications in computer science, engineering, economics, healthcare, and logistics, making it interesting for practitioners facing complex decision-making problems in these areas.