This book constitutes the proceedings of the International Joint Conference on Rules and Reasoning, RuleML+RR 2021, held in Leuven, Belgium, during September, 2021. This is the 5th conference of a new series, joining the efforts of two existing conference series, namely "e;RuleML"e; (International Web Rule Symposium) and "e;RR"e; (Web Reasoning and Rule Systems).The 17 full research papers presented together with 2 short technical communications papers and 2 abstracts of invited papers were carefully reviewed and selected from 39 submissions.