This should get you started (untested):

use strict;
use warnings;

my %conn;

while(<>){
  next unless  my ($c) = m/conn=(\d+)\s/;
  m/ connection from ([\d\.]+) to ([\d\.]+) port (\d+)/ and do{
    $conn{$c}{FROM}=$1;
    $conn{$c}{TO}  =$2;
    $conn{$c}{PORT}=$3;
    next;
  };
  m/BIND dn="([^"]*)"/ and do{
     $conn{$c}{BINDDN}=$1;
     next;
  } 
}

for (sort keys %conn){
  print "Connection $_  $conn{$_}{FROM} -> $conn{$_}{TO} \[$conn{$_}{P
+ORT}\] DN=$conn{$_}{BINDDN};\n";
}
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Update:Fixed typo for $2, and added print logic.
Update2: Fixed syntax (Missing semicolon), and allowed for empty DN