  We present theory of dc Josephson effect in contacts between Fe-based and
spin-singlet $s$-wave superconductors. The method is based on the calculation
of temperature Green's function in the junction within the tight-binding model.
We calculate the phase dependencies of the Josephson current for different
orientations of the junction relative to the crystallographic axes of Fe-based
superconductor. Further, we consider the dependence of the Josephson current on
the thickness of an insulating layer and on temperature. Experimental data for
PbIn/Ba$_{1-x}$K$_{x}$(FeAs)$_2$ point-contact Josephson junctions are
consistent with theoretical predictions for $s_{\pm}$ symmetry of an order
parameter in this material. The proposed method can be further applied to
calculations of the dc Josephson current in contacts with other new
unconventional multiorbital superconductors, such as $Sr_2RuO_4$ and
superconducting topological insulator $Cu_xBi_2Se_3$.
