The bottleneck in your program seems the sorting at the end. Sorting is super-linear, which means that if your input size doubles, the running time more than doubles.

I'd write your program slightly different, but that shouldn't make much of a difference:

my (%hash, $line);
while ($line = <STDIN>) {
    while (my ($word) = (lc $word) =~ /[a-z]{2,}/g) {
        next if $word =~ /(.)\1\1\1\1/;
        $hash{$word}++;
    }
}
print "$_\n" for sort keys %hash;
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Now, if the words are in order, there's no need for the hash, or the sorting:

my ($line, $prev);
$prev = "";
while ($line = <STDIN>) {
    while (my ($word) = (lc $word) =~ /[a-z]{2,}/g) {
        next if $word =~ /(.)\1\1\1\1/;
        next if $word eq $prev;
        print "$word\n";
        $prev = $word;
    }
}
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(Code fragments are untested)