  We analyze the pentagon transitions involving arbitrarily many flux-tube
gluonic excitations and bound states thereof in planar N=4 Super-Yang-Mills
theory. We derive all-loop expressions for all these transitions by
factorization and fusion of the elementary transitions for the lightest gluonic
excitations conjectured in a previous paper. We apply the proposals so obtained
to the computation of MHV and NMHV scattering amplitudes at any loop order and
find perfect agreement with available perturbative data up to four loops.
