  For the iron-based high $T_c$ superconductor LaFeAsO$_{1-x}$F$_x$, we
construct a minimal model, where all of the five Fe $d$ bands turn out to be
involved. We then investigate the origin of superconductivity with a five-band
random-phase approximation by solving the Eliashberg equation. We conclude that
the spin fluctuation modes arising from the nesting between the disconnected
Fermi pockets realise, basically, an extended s-wave pairing, where the gap
changes sign across the nesting vector.
