  We study multiplicity of the eigenvalues of the Hodge Laplacian on smooth,
compact Riemannian manifolds of dimension five for generic families of metrics.
We prove that generically the Hodge Laplacian, restricted to the subspace of
co-exact two-forms, has nonzero eigenvalues of multiplicity two. The proof is
based on the fact that Hodge Laplacian restricted to the subspace of co-exact
two-forms is minus the square of the Beltrami operator, a first-order operator.
We prove that for generic metrics the spectrum of the Beltrami operator is
simple. Because the Beltrami operator in this setting is a skew-adjoint
operator, this implies the main result for the Hodge Laplacian.
