  We show that for a real-analytic connected holomorphically nondegenerate
5-dimensional CR-hypersurface $M$ and its symmetry algebra $\mathfrak{s}$ one
has either: (i) $\dim\mathfrak{s}=15$ and $M$ is spherical (with Levi form of
signature either $(2,0)$ or $(1,1)$ everywhere), or (ii)
$\dim\mathfrak{s}\le11$ where $\dim\mathfrak{s}=11$ can only occur if on a
dense open subset $M$ is spherical with Levi form of signature $(1,1)$.
Furthermore, we construct a series of examples of pairwise nonequivalent
CR-hypersurfaces with $\dim\mathfrak{s}=11$.
