  We consider the superspace of D=3, N=5 supersymmetry using SO(5)/U(2)
harmonic coordinates. Three analytic N=5 gauge superfields depend on three
vector and six harmonic bosonic coordinates and also on six Grassmann
coordinates. Decomposition of these superfields in Grassmann and harmonic
coordinates yields infinite-dimensional supermultiplets including a
three-dimensional gauge Chern-Simons field and auxiliary bosonic and fermionic
fields carrying SO(5) vector indices. The superfield action of this theory is
invariant with respect to D=3, N=6 conformal supersymmetry realized on N=5
superfields.
