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

K-theory for the Leaf Spaces of the Orbit Foliations of the co-adjoint Action of some 5-dimensional Solvable Lie groups