  This paper extends joint work with R. Friedman to show that the closure of
the locus of intermediate Jacobians of smooth cubic threefolds, in the moduli
space of principally polarized abelian varieties (ppav's) of dimension five, is
an irreducible component of the locus of ppav's whose theta divisor has a point
of multiplicity three or more. This paper also gives a sharp bound on the
multiplicity of a point on the theta divisor of an irreducible ppav of
dimension less than or equal to five; for dimensions four and five, this
improves the bound due to J. Koll\'ar, R. Smith-R. Varley, and L. Ein-R.
Lazarsfeld.
