Have you tried removing the starting point for your LIMIT (as it starts from 0 anyway 🆒
<HTML>
<BODY>
<?
$db = mysql_connect("localhost", "pixel_pixel", "8651vivo");
mysql_select_db("news", $db);
$query = mysql_query("SELECT date, headline, text FROM news ORDER BY date DESC LIMIT 5", $db);
while($data = mysql_fetch_array($query)){
echo "<B>$data[1]</B> - ";
echo date("j/n - Y", $data[0]);
echo "<BR>$data[2]<BR><BR>";
}
?>
</BODY>
</HTML>
The only other thing I've done is to redeclare your $db connection within the sql. Your query is almost identical to one of mine in a news script which is as follows (only difference being the lack of $db in your original).
$headlines_result = mysql_query("SELECT news_id,news_title,news_date FROM $newstable WHERE news_status = 1 ORDER BY news_id DESC LIMIT 5",$db);