  Vacuum solutions admitting a hypersurface-orthogonal repeated principal null
direction are an important class of 4d algebraically special spacetimes. We
investigate the 5d analogues of such solutions: vacuum spacetimes admitting a
hypersurface-orthogonal multiple Weyl aligned null direction (WAND). Such
spacetimes fall into 4 families determined by the rank of the 3X3 matrix that
defines the expansion and shear of the multiple WAND. The rank 3 and rank 0
cases have been studied previously. We investigate the 2 remaining families. We
show how to define coordinates which lead to a considerable simplification of
the Einstein equation with cosmological constant. The rank 2 case gives warped
product and Kaluza-Klein versions of the 4d Robinson-Trautman solutions as well
as some new solutions. The rank 1 case gives product, or analytically continued
Schwarzschild, spacetimes.
