  Monte Carlo results for the moments <M^k> of the magnetization distribution
of the nearest-neighbor Ising ferromagnet in a L^d geometry, where L (4 \leq L
\leq 22) is the linear dimension of a hypercubic lattice with periodic boundary
conditions in d=5 dimensions, are analyzed in the critical region and compared
to a recent theory of Chen and Dohm (CD) [X.S. Chen and V. Dohm, Int. J. Mod.
Phys. C (1998)]. We show that this finite-size scaling theory (formulated in
terms of two scaling variables) can account for the longstanding discrepancies
between Monte Carlo results and the so-called ``lowest-mode'' theory, which
uses a single scaling variable tL^{d/2} where t=T/T_c-1 is the temperature
distance from the critical temperature, only to a very limited extent. While
the CD theory gives a somewhat improved description of corrections to the
``lowest-mode'' results (to which the CD theory can easily be reduced in the
limit t \to 0, L \to \infty, tL^{d/2} fixed) for the fourth-order cumulant,
discrepancies are found for the susceptibility (L^d <M^2>). Reasons for these
problems are briefly discussed.
