This volume contains the proceedings of the 5th MSJ Seasonal Institute on Schubert Calculus, held at Osaka City University, from September 17-27, 2012. It is recommended for all researchers and graduate students who are interested in Schubert calculus and its many connections and applications to related areas of mathematics, such as geometric representation theory, combinatorial aspects of algebraic varieties arising in Lie theory, and equivariant topology. Alain Lascoux, one of the pioneers of modern Schubert calculus and a contributor to this volume, passed away during the time of the editing process of the proceedings. This volume is dedicated to him.