diff --git a/src/wp-includes/PHPMailer/PHPMailer.php b/src/wp-includes/PHPMailer/PHPMailer.php
index 7457f88488..25b04e42d0 100644
--- a/src/wp-includes/PHPMailer/PHPMailer.php
+++ b/src/wp-includes/PHPMailer/PHPMailer.php
@@ -750,7 +750,7 @@ class PHPMailer
      *
      * @var string
      */
-    const VERSION = '6.5.3';
+    const VERSION = '6.5.4';
 
     /**
      * Error severity: message only, continue processing.
@@ -1185,6 +1185,7 @@ class PHPMailer
      *
      * @param string $addrstr The address list string
      * @param bool   $useimap Whether to use the IMAP extension to parse the list
+     * @param string $charset The charset to use when decoding the address list string.
      *
      * @return array
      */
@@ -1744,7 +1745,7 @@ class PHPMailer
                 fwrite($mail, $header);
                 fwrite($mail, $body);
                 $result = pclose($mail);
-                $addrinfo = static::parseAddresses($toAddr, true, $this->charSet);
+                $addrinfo = static::parseAddresses($toAddr, true, $this->CharSet);
                 $this->doCallback(
                     ($result === 0),
                     [[$addrinfo['address'], $addrinfo['name']]],
@@ -1799,7 +1800,13 @@ class PHPMailer
      */
     protected static function isShellSafe($string)
     {
-        //Future-proof
+        //It's not possible to use shell commands safely (which includes the mail() function) without escapeshellarg,
+        //but some hosting providers disable it, creating a security problem that we don't want to have to deal with,
+        //so we don't.
+        if (!function_exists('escapeshellarg') || !function_exists('escapeshellcmd')) {
+            return false;
+        }
+
         if (
             escapeshellcmd($string) !== $string
             || !in_array(escapeshellarg($string), ["'$string'", "\"$string\""])
@@ -1907,7 +1914,7 @@ class PHPMailer
         if ($this->SingleTo && count($toArr) > 1) {
             foreach ($toArr as $toAddr) {
                 $result = $this->mailPassthru($toAddr, $this->Subject, $body, $header, $params);
-                $addrinfo = static::parseAddresses($toAddr, true, $this->charSet);
+                $addrinfo = static::parseAddresses($toAddr, true, $this->CharSet);
                 $this->doCallback(
                     $result,
                     [[$addrinfo['address'], $addrinfo['name']]],
@@ -2632,16 +2639,15 @@ class PHPMailer
             $result .= $this->headerLine('X-Priority', $this->Priority);
         }
         if ('' === $this->XMailer) {
+            //Empty string for default X-Mailer header
             $result .= $this->headerLine(
                 'X-Mailer',
                 'PHPMailer ' . self::VERSION . ' (https://github.com/PHPMailer/PHPMailer)'
             );
-        } else {
-            $myXmailer = trim($this->XMailer);
-            if ($myXmailer) {
-                $result .= $this->headerLine('X-Mailer', $myXmailer);
-            }
-        }
+        } elseif (is_string($this->XMailer) && trim($this->XMailer) !== '') {
+            //Some string
+            $result .= $this->headerLine('X-Mailer', trim($this->XMailer));
+        } //Other values result in no X-Mailer header
 
         if ('' !== $this->ConfirmReadingTo) {
             $result .= $this->headerLine('Disposition-Notification-To', '<' . $this->ConfirmReadingTo . '>');
diff --git a/src/wp-includes/PHPMailer/SMTP.php b/src/wp-includes/PHPMailer/SMTP.php
index 676dba2923..138177060e 100644
--- a/src/wp-includes/PHPMailer/SMTP.php
+++ b/src/wp-includes/PHPMailer/SMTP.php
@@ -35,7 +35,7 @@ class SMTP
      *
      * @var string
      */
-    const VERSION = '6.5.3';
+    const VERSION = '6.5.4';
 
     /**
      * SMTP line break constant.
@@ -187,6 +187,7 @@ class SMTP
         'SendGrid' => '/[\d]{3} Ok: queued as (.*)/',
         'CampaignMonitor' => '/[\d]{3} 2.0.0 OK:([a-zA-Z\d]{48})/',
         'Haraka' => '/[\d]{3} Message Queued \((.*)\)/',
+        'Mailjet' => '/[\d]{3} OK queued as (.*)/',
     ];
 
     /**