Answer:
The best known are abstemious and facetious. Others include the rare botanical words acheilous, anemious, and caesious, the rare zoological word annelidous, and the chemical term arsenious.
Note, though, that the premise of the question is wrong. English has six vowels, because 'y' is commonly used as a vowel in English. In fact, you can add the 'ly' suffix to any of the above words to create an English word with all six vowels in order. (Some consider 'w' a vowel too, but 'w' by itself never functions as a vowel in English, aside from a couple of obscure borrowings from Welsh.)