"Max" wrote...
Try something like:

=AVERAGE(IF(A1:A5MIN(A1:A5),A1:A5))

Array-enter the formula, i.e. press CTRL+SHIFT+ENTER
instead of just pressing ENTER
....

If there are multiple instances of the smallest value, this may not produce
the desired result. Indeed, if all cells are equal, this will return #DIV/0!

If the OP only wants to eliminate a single smallest value, then (general)

=SUM(A1:A5,-MIN(A1:A5))/(COUNT(A1:A5)-1)

or if the range has relatively few cells,

=AVERAGE(LARGE(A1:A5,{1;2;3;4}))