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This fifth volume on Advances and Applications of DSmT for Information Fusion collects theoretical and applied contributions of researchers working in different fields of applications and in mathematics, and is available in open-access. The collected contributions of this volume have either been published or presented after disseminating the fourth volume in 2015 (available at fs.unm.edu/DSmT-book4.pdf or www.onera.fr/sites/default/files/297/2015-DSmT-Book4.pdf) in international conferences, seminars, workshops and journals, or they are new. The contributions of each part of this volume are chronologically ordered. First Part of this book presents some theoretical advances on DSmT, dealing mainly with modified Proportional Conflict Redistribution Rules (PCR) of combination with degree of intersection, coarsening techniques, interval calculus for PCR thanks to set inversion via interval analysis (SIVIA), rough set classifiers, canonical decomposition of dichotomous belief functions, fast PCR fusion, fast inter-criteria analysis with PCR, and improved PCR5 and PCR6 rules preserving the (quasi-)neutrality of (quasi-)vacuous belief assignment in the fusion of sources of evidence with their Matlab codes. Because more applications of DSmT have emerged in the past years since the apparition of the fourth book of DSmT in 2015, the second part of this volume is about selected applications of DSmT mainly in building change detection, object recognition, quality of data association in tracking, perception in robotics, risk assessment for torrent protection and multi-criteria decision-making, multi-modal image fusion, coarsening techniques, recommender system, levee characterization and assessment, human heading perception, trust assessment, robotics, biometrics, failure detection, GPS systems, inter-criteria analysis, group decision, human activity recognition, storm prediction, data association for autonomous vehicles, identification of maritime vessels, fusion of support vector machines (SVM), Silx-Furtif RUST code library for information fusion including PCR rules, and network for ship classification. Finally, the third part presents interesting contributions related to belief functions in general published or presented along the years since 2015. These contributions are related with decision-making under uncertainty, belief approximations, probability transformations, new distances between belief functions, non-classical multi-criteria decision-making problems with belief functions, generalization of Bayes theorem, image processing, data association, entropy and cross-entropy measures, fuzzy evidence numbers, negator of belief mass, human activity recognition, information fusion for breast cancer therapy, imbalanced data classification, and hybrid techniques mixing deep learning with belief functions as well. We want to thank all the contributors of this fifth volume for their research works and their interests in the development of DSmT, and the belief functions. We are grateful as well to other colleagues for encouraging us to edit this fifth volume, and for sharing with us several ideas and for their questions and comments on DSmT through the years. We thank the International Society of Information Fusion (www.isif.org) for diffusing main research works related to information fusion (including DSmT) in the international fusion conferences series over the years. Florentin Smarandache is grateful to The University of New Mexico, U.S.A., that many times partially sponsored him to attend international conferences, workshops and seminars on Information Fusion. Jean Dezert is grateful to the Department of Information Processing and Systems (DTIS) of the French Aerospace Lab (Office National d’E´tudes et de Recherches Ae´rospatiales), Palaiseau, France, for encouraging him to carry on this research and for its financial support. Albena Tchamova is first of all grateful to Dr. Jean Dezert for the opportunity to be involved during more than 20 years to follow and share his smart and beautiful visions and ideas in the development of the powerful Dezert-Smarandache Theory for data fusion. She is also grateful to the Institute of Information and Communication Technologies, Bulgarian Academy of Sciences, for sponsoring her to attend international conferences on Information Fusion.