  We write the Lagrangian of the general N=5 three-dimensional superconformal
Chern-Simons theory, based on a basic Lie superalgebra, in terms of our
recently introduced N=5 three-algebras. These include N=6 and N=8
three-algebras as special cases. When we impose an antisymmetry condition on
the triple product, the supersymmetry automatically enhances, and the N=5
Lagrangian reduces to that of the well known N=6 theory, including the ABJM and
ABJ models.
