  An earlier four-loop calculation of the fluctuation pressure of a fluid
membrane between two infinite walls is extended to five loops. Variational
perturbation theory is used to extract the hard-wall limit from perturbative
results obtained with a smooth potential. Comparison with a structurally
similar quantum mechanics problem of a particle in a box is used for an
alternative way of extracting the membrane pressure and also to estimate the
quality of the results. Our values lie above the best available Monte Carlo
data.
