The Mathematics Pentathlon is a tournament of mathematics games held each spring since 1979 to promote the development of mathematical concepts and skills while fostering interaction among the educational community. There are five games in each of four divisions, for grades K-1, 2-3, 4-5, and 6-7. The focus is on active problem solving and critical thinking skills for children at different ability levels. This manual for grades 4-5 first discusses problem solving, educational community involvement, the range of academic performance, and the use of physical models. Then each game is described, with mathematical content, materials, time, goals, starting procedures, game rules, and tournament rules stated, plus a reproduction of the gameboard. The games for this level are Contig 60, Juggle, Stars and Bars, Queen's Guard, and Fab. (MNS)