If all the email addresses are enclosed in brackets then perhaps use a simple regex to extract them. Here is a basic test script to play around with. The added confirm checkbox lets you test before actually sending.

#!C:/Perl/bin/perl -w
use strict;
use CGI ':standard';

my $MAX = 10; # maximum in list
my %list = ();
my $confirm    = param('confirm');
my $Email_List = param('Email_List');

# extract email adressess between ()
while ( $Email_List =~ m/\(([^)]+)/g ){
  my $addr = $1;
  
  # remove spaces and any other cleaning here
  # assuming you don't have unusual addresses like
  # "Any Person"@somewhere.com
  $addr =~ s/ //g; 
  
  # check valadity
  if ( is_valid($addr) ){
    $list{$addr} = 'Not sent'; #  using key avoids duplicates
  }    
}

# check not too many
my $msg;
my $no = scalar(keys %list);
if ($no > $MAX){
  $msg = "ERROR - $no is too many to send";
} else {
  # send emails if confirm checked
  if ($confirm){
    for (keys %list){
      $list{$_} = send_to($_); # store result
    }
  }
}

# input form 
print header(), start_html;
print qq!<h4>Recipients (maximum $MAX)</h4>
<form action="" method="post">
<textarea cols="80" rows="20" name="Email_List">
$Email_List
</textarea><br/>
<br/>
Confirm<input name="confirm" type="checkbox"/>
<input type="submit" name="action" value="Send"/>
</form><br/>
<span style="background-color:#ffff00">$msg</span>!;
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# present result in a table
print '<table border="1" cellspacing="0" cellpadding="5">';
my $n = 0;
for  (sort keys %list){
  ++$n;
  print qq!<tr>
    <td>$n</td>
    <td>$_</td>
    <td>$list{$_}</td>
  </tr>!;
}
print '</table><br/>';
print scalar localtime;
print end_html;

# your email routine here
sub send_to {
  my $to = shift;
  my $result = "Log or error for $to";
#  $mail{To} = $to;
#  if ( sendmail(%mail) ){
#    $result = $Mail::Sendmail::log;
#  } else {
#    $result = $Mail::Sendmail::error;
#  }
  return $result; # either log or error msg
}

# check address is valid
sub is_valid {
  my $addr = shift;
  # make checks here as 
  # complicated  as required
  if ($addr =~ /\@/){
    return 1;
  } 
  return 0;  
}
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