Without testing (no Perl on this machine...), I am willing to bet that your code does not work. 100 is going to sort first because sort is lexigraphical. But here is an alternate solution that should work fine even for long sequences.

my @original_array = qw(5, 100, 2, 8, 40);

# Build lookup hash
my %num2letter;
my $char = "A";
foreach my $num (sort {$a <=> $b} @original_array) {
  $num2letter{$num} = $char++;
}

my @letter_sequence = @num2letter{@original_array};
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(Note - if you are looping over an array searching for something, then you probably wanted a hash...)

Update: Change map to a more efficient slice as suggested by Aristotle, remove accidental space within a my.