The concept of Society 5.0 and Industry 5.0 is not a simple chronological continuation or alternative to Industry 4.0 paradigm. Society 5.0 aims to place human beings at the midpoint of innovation, exploiting the impact of technology and Industry 4.0 results with the technological integration to improve quality of life, social responsibility and sustainability. This ground-breaking perspective has common points with the objectives of the United Nations Sustainable Development Goals. It also has major implication for universities transformations. Universities are called upon producing knowledge for new technologies and social innovation. In our paper, we argue that digitalisation opens new perspectives for universities and can become one of the main drivers of their change. Incorporating the assumptions of Society 5.0 and Industry 5.0 into the universities practices and policies will allow both universities and societies to fully benefit from digital transformation. Making the human-oriented innovation as the universities trademark and developing new cooperative models will also help to achieve sustainable priorities. The use of the Quintuple Helix Model (QHM) might foster the process of necessary transformations capacities as it integrates different perspectives and sets the stage for sustainability priorities and considerations. As far as the practical goal is concerned, the paper proposes a set of recommendations for universities aiming at developing new forms and channels of distribution of education, research and innovation within in the context of QHM and Society 5.0. We call them socially and digitally engaged model.