Simple check next unless $_; as a second line of the while cycle will do. All whitespaces from the beginning of the line were removed by $_ =~ s/^\s+//;, so $_ is empty at that time if it only contained whitespace (or nothing).

UPDATE: And regarding the duplicate "5", you'll have to trim the trailing whitespace characters as well. s/\s+$//; will help with that. For the sake of your education :-), that means: in $_, if there is a sequence of 1 or more (that's the +) whitespace characters(\s) occuring just before the end of the string ($), replace it (s/.../.../) with nothing (the nothing between the last two slashes)

UPDATE2: As pointed out by moritz, you'll have to add a newline to the print statement if all trailing whitespaces including the newline were trimmed. The body of the while loop will look like

      s/^\s+//;
      s/\s+$//;
      next unless $_;
      $seen{$_}++;
      next if $seen{$_} > 1;
      print "$_\n";
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