  In this paper, combining Kirillov's method of orbits with Connes' method in
Differential Geometry, we study the so-called MD(5,3C)-foliations, i.e. the
orbit foliations of the co-adjoint action of MD(5,3C)-groups. First, we
classify topologically MD(5,3C)-foliations based on the classification of all
MD(5,3C)-algebras in [22] and the picture of co-adjoint orbits (K-orbits) of
all MD(5,3C)-groups in [23]. Finally, we study K-theory for leaf space of
MD(5,3C)-foliations and describe analytically or characterize Connes'
C*-algebras of the considered foliations by KK-functors.
