  In this paper we study the geometry of simply connected two-step nilpotent
Lie groups of dimension five. We give the Levi-Civita connection, curvature
tensor, sectional and scalar curvatures of these spaces and show that they have
constant negative scalar curvature. Also we show that the only space which
admits left invariant Randers metric of Berwald type has three dimensional
center. In this case the explicit formula for computing flag curvature is
obtained and it is shown that flag curvature and sectional curvature have the
same sign.
