  We construct the D=3, N=5 harmonic superspace using the SO(5)/U(1) x U(1)
harmonics. Three gauge harmonic superfields satisfy the off-shell constraints
of the Grassmann and harmonic analyticities. The corresponding component
supermultiplet contains the gauge field A_m and an infinite number of bosonic
and fermionic fields with the SO(5) vector indices arising from decompositions
of gauge superfields in harmonics and Grassmann coordinates. The nonabelian
superfield Chern-Simons action is invariant with respect to the N=6
superconformal supersymmetry realized on the N=5 superfields. The component
Lagrangian contains the Chern-Simons interaction of A_m and an infinite number
of bilinear and trilinear interactions of auxiliary fields. The fermionic and
bosonic auxiliary fields from the infinite N=5 multiplet vanish on-shell.
