mysql php : switching between mysql databases is slow

function getUserarchive( $userid) {
  $out= "";
  $dbname = 'Faxarchive';
  $db = mysql_select_db($dbname);
  $sql = "select sent, received from faxarchivetable where userid = '" . $userid . "'";

  if ( $rs = mysql_query($sql) {
    while ($row = mysql_fetch_array($rs) ) {
      $out = $row['sent'] . " " . $row['received'];
    }//end while
  }//end if query

  return ($out);
}//end function


$conn = mysql_connect($dbhost, $dbuser, $dbpass) or die ('Error connecting to mysql');

$dbname = 'Faxusers';
$db = mysql_select_db($dbname);
$sql="select distinct userid from faxuserstable";
if ( $rs = mysql_query($sql) {
  while ($row = mysql_fetch_array($rs) ) {
    $out = $row['userid'] . ":" . getuserarchive($row['userid']);
  }//end while
}//end if query

SELECT sent, received
FROM Faxarchive.faxarchivetable
WHERE userid IN ( SELECT DISTINCT userid FROM Faxusers.faxuserstable );