Monte Carlo simulations, using the PERM algorithm, of interacting
self-avoiding walks (ISAW) and interacting self-avoiding trails (ISAT) in five
dimensions are presented which locate the collapse phase transition in those
models. It is argued that the appearance of a transition (at least) as strong
as a pseudo-first-order transition occurs in both models. The values of various
theoretically conjectured dimension-dependent exponents are shown to be
consistent with the data obtained. Indeed the first-order nature of the
transition is even stronger in five dimensions than four. The agreement with
the theory is better for ISAW than ISAT and it cannot be ruled out that ISAT
have a true first-order transition in dimension five. This latter difference
would be intriguing if true. On the other hand, since simulations are more
difficult for ISAT than ISAW at this transition in high dimensions, any
discrepancy may well be due to the inability of the simulations to reach the
true asymptotic regime.Comment: LaTeX file, 16 pages incl. 7 figure