I have been dealing whit this problem for a wile, I tryed whit a hotmail address and it works whit no problem, but gmail it was a big problem for me.
What I did?
Well, first I go to my install path: C:\inetpub\wwwroot\moodle3.3\lib\phpmailer
And I make a copy of the file class.smtp.php.
and add two lines of code at line 255 approximately, it looks like this:
_____________________________________________________________________________________________________
public function connect($host, $port = null, $timeout = 30, $options = array())
{
if(count($options)==0){
$options["ssl"]=array("verify_peer"=>false,"verify_peer_name"=>false,"allow_self_signed"=>true);
}
__________________________________________________________________________________________________
and second:
go to this link https://myaccount.google.com/device-activity?hl=en&pli=1
and view recent attempts to use the account and accept suspicious access.
(If you don´t use google You don´t have to do this).
I dont know if it is the best thing to do, because the phpmailer is looking for a certificate on local host and I disable the ssl check whit this, but at least now I can send emails.
credits for this guys:
http://punto50.blogspot.com/2015/03/envio-de-correo-con-phpmailer-y-gmail.html
I hove this can help some one else. (sorry for my bad English)
Happy New year 2018 to all of you!