  We construct the Grassmann-analytic gauge superfields in D=3, N=5 harmonic
superspace using the SO(5)/U(1)xU(1) harmonics. These gauge N=5 superfields
contain an infinite number of bosonic and fermionic fields arising from
decompositions in harmonics and Grassmann coordinates. The bosonic sector of
this supermultiplet includes the gauge field A_m, the additional nongauge
vector field B_m, the scalar field S, two SO(5)-vector scalar fields and an
infinite number of auxiliary fields with SO(5) indices. The nonabelian
Chern-Simons-type action in the N=5 analytic harmonic superspace is
constructed. This action is also invariant with respect to the sixth
supersymmetry realized on the N=5 gauge superfields. The component Lagrangian
describes the scale-invariant nontrivial interactions of the gauge Chern-Simons
field A_m with B_m, S and other basic and auxiliary fields. All auxiliary
fields can be excluded from this Lagrangian.
