I’m not sure what’s your situation,.. Anyway try to ask your provider to allow additional ports for you. It’s common practice to earn trust first,.. Also you can set up PHPMailer to use this port, assuming that your SMTP provider is server you are trying to connect, and by enforcing this port provider is using tls instead of ssl,..
$smtp = new PHPMailer(TRUE);
$smtp->IsSMTP();
...
$smtp->SMTPSecure = 'tls';
$smtp->Port = 587;
...
$smtp->Send()