This handbook surveys the computational and algorithmic problems of systems of applied reasoning. The various theoretical and modelling aspects of defeasible reasoning were dealt with in the first four volumes, and this volume now turns to the algorithmic aspect. Topics covered include: Computation in valuation algebras; consequence finding algorithms; possibilistic logic; probabilistic argumentation systems, networks and satisfiability; algorithms for imprecise probabilities, for Dempster-Shafer, and network based decisions.