That should be pretty simple:
$order_date_plus_five = zen_datetime_short(date('Y-m-d H:i:s', strtotime($orders->fields['date_purchased']) + 5 * 24 * 3600 ));
That is, assuming your $orders->fields['date_purchased']
is in the format of Y-m-d H:i:s
that is the standard format for mysql datetime format.
The main idea is that php's strtotime
function generated a timestamp from a datetime string. After you generate that timestamp, you just add the number of seconds of 5 days (5 * 24 * 3600
)