You do not have to get the jewels in any particular order, so the last of the 5 jewels could be any of them.
(see the related question)
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There is no known security code on Nabooti Island.
Feed it the cactus fruit you got from Mountains of the Moon.
The Moonstone is in Vince's Bag. Distract him by calling his number on your cell phone (it's on the shovel : 555-6789).
It depends on which jewel you need. The first jewel that you obtain is Alfred's Jewel. This is located by his dead body. The 2nd jewel that you obtain is Alexander's Jewel. You can get this when it falls off of Alexander's body. The final jewel you get after you defeat Alexia.
you have to know and talk to Jewel Kilcher