How do I do calendar arithmetic with java.util.Date?

You could use Calendar, which will make it easy to add any length of time:

Calendar cal = Calendar.getInstance();
cal.setTime(date);
cal.add(Calendar.MINUTE, 5);
Date newDate = cal.getTime();

For your case you could just add the time in milliseconds like this:

Date newDate = new Date(date.getTime() + 5 * 60 * 1000L);