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 speci.