Yes, you are correct to a point. If you are under 16, then the passport is only good for 5 years. Here
is the link to the FAQ's site on the United Stated Department of State site.
Also, as an FYI, when you renew your passport, you have to send in your old one, but don't worry. You'll get it back with holes punched in it to show it is void. This way, you can still look back at the places you have visited if it's stamped
. In our cases, most cruise lines just swipe it at check in, so there are no stamps!