  Let N be a simply connected, connected real nilpotent Lie group of finite
dimension n. We study subgroups $\Gamma$ in $\Aff (N)=N\rtimes \Aut (N)$ acting
properly discontinuously and cocompactly on N. This situation is a natural
generalization of the so-called affine crystallographic groups. We prove that
for all dimensions $1\le n\le 5$ the generalized Auslander conjecture holds,
i.e., that such subgroups are virtually polycyclic.
