This line has some problems:

while (my ($word) = (lc $word) =~ /[a-z]{2,}/g) {
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It won't compile under use strict; ... i think you meant to pattern match against lc $line, and there's no parens in the regex to capture anything ...

Working off your general idea, i came up with (no clue how this rates performance-wise against OP or my other solution below):

my %hash;
while (my $line = <STDIN>) {
    foreach my $word  ( $line =~ m/\b([a-zA-Z]{2,4})\b/g ) {
        $hash{lc $word}++;
    }
}
print "$_\n" for sort keys %hash;
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Which can be rewritten as:

while (my $line = <STDIN>) {
    $hash{lc $_}++ for $line =~ m/\b([a-zA-Z]{2,4})\b/g;
}
#or
do { $hash{lc $_}++ for m/\b([a-zA-Z]{2,4})\b/g } for <STDIN>;
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Update: Doh. note i misread the /(\w)\1\1\1\1/ regex as 5+ letters instead of 5+ of the _same_ letter in a row .. If the 5+ letters don't happen very often, might be better to just exclude at the end:

while (my $line = <STDIN>) {
    $hash{lc $_}++ for $line =~ m/([a-zA-Z]{2,})/g;
}
delete $hash{$_} for grep /(\w)\1{4}/, keys %hash;
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