$re = '/s:\d+:"themes";s:\d+:"[\w,\s]*(\bbusinessman\b)[\w,\s]*";/i';
$str = 'a:4:{s:5:"dates";a:2:{s:7:"created";s:27:"2017-11-03T01:14:56.582259Z";s:8:"imported";s:27:"2017-11-03T01:14:56.582259Z";}s:11:"displayName";s:12:"Donald Trump";s:11:"description";s:17:"Donald John Trump";s:6:"themes";s:10:"apple, Businessman, Politician";}';
preg_match($re, $str, $matches, PREG_OFFSET_CAPTURE, 0);
// Print the entire match result
var_dump($matches);
Please keep in mind that these code samples are automatically generated and are not guaranteed to work. If you find any syntax errors, feel free to submit a bug report. For a full regex reference for PHP, please visit: http://php.net/manual/en/ref.pcre.php