1. by setting 2 values to $sql, you are overiding the first sql string..
2. you are receving this error because you have not wrapped your values in quotes.. the only time in sql that you do not need to wrap a value in quotes is if its an integer..and even then its not a bad idea to..
include("server.php");
$sql = "UPDATE players SET points = points + 5 WHERE is_active = 1 ORDER BY score DESC LIMIT 50";
$sql1 = "INSERT INTO credit_logs(player_id,Description,amount,end_balance) VALUES ('$playerID','top 50 finish',5,5)";
$query = mysql_query($sql) or die(mysql_error());
$query1 = mysql_query($sql1) or die(mysql_error());
if($query && $query1){ //if both queries are successful
echo "Prizes Paid";
}