Error sending bulk emails to users: Too many messages in this connection laravel 5.2

I am trying to send bulk emails (approx. 5000) to subscriber. I am sending all emails in BCC and Mail::queue(). I am running command from console to trigger emails.

try {
$bccEmails = ['test@test.com', 'xyz@gmail.com', 'abc@gmail.com', 'anb@hotmail.com', 'xyzz@yahoo.com'];

Mail::queue('Emails.Newsletter', $data, 
    function ($message) use ($bccEmails, $subject) {

      $message->from('no-reply@test.com', 'xyz.com')
              ->bcc($bccEmails)
              ->replyTo($this->adminEmail, $this->adminName)
              ->subject($subject);
});

} catch (Exception $ex) {
   Log::info("Email sending error: ".$ex->getMessage());
}

But i am getting error as below:

"Expected response code 250 but got code "421", with message "421 too many messages in this connection"

1. How to resolve above issue ?

2. What is the best way to send bulk emails to users ?

Second question: which one is the best approach. As mentioned above Mail:queue or Mail:send in loop as below:

$toEmails = ['test@test.com', 'xyz@gmail.com', 'abc@gmail.com', 'anb@hotmail.com', 'xyzz@yahoo.com'];

foreach ($toEmails as $key => $email) {

   try {
    Mail::send('Emails.Newsletter', $data, 
    function ($message) use ($email, $subject) {

      $message->from('no-reply@test.com', 'xyz.com')
              ->to($email)
              ->replyTo($this->adminEmail, $this->adminName)
              ->subject($subject);
    });

  } catch (Exception $ex) {
    Log::info("Email sending error: ".$ex->getMessage());
    // If failed continue sending next email
  }

} 

Using: Laravel 5.2, Shared hosting

Please help on this. Let me know if further details is required.

via Chebli Mohamed