Argumentation, which has long been a topic of study in philosophy, has become a well-established aspect of computing science in the last 20 years.This book presents the proceedings of the fifth conference on Computational Models of Argument (COMMA), held in Pitlochry, Scotland in September 2014. Work on argumentation is broad, but the COMMA community is distinguished by virtue of its focus on the computational and mathematical aspects of the subject. This focus aims to ensure that methods are sound - that they identify arguments that are correct in some sense - and provide an unambiguous specification for implementation; producing programs that reason in the correct way and building systems capable of natural argument or of recognizing argument.The book contains 24 long papers and 18 short papers, and the 21 demonstrations presented at the conference are represented in the proceedings either by an extended abstract or by association with another paper.The book will be of interest to all those whose work involves argumentation as it relates to artificial intelligence.