  The finite size scaling behaviour for the Ising model in five dimensions,
with either free or cyclic boundary, has been the subject for a long running
debate. The older papers have been based on ideas from e.g. field theory or
renormalization. In this paper we propose a detailed and exact scaling picture
for critical region of the model with cyclic boundary. Unlike the previous
papers our approach is based on a comparison with the existing exact and
rigorous results for the FK-random-cluster model on a complete graph. Based on
those results we identify several distinct scaling regions in an $L$-dependent
window around the critical point. We test these predictions by comparing with
data from Monte Carlo simulations and find a good agreement. The main feature
which differs between the complete graph and the five dimensional model with
free boundary is the existence of a bimodal energy distribution near the
critical point in the latter. This feature was found by the same authors in an
earlier paper in the form of a quasi-first order phase transition for the same
Ising model.
