The word Iouea (a genus of sea sponges)is the shortest word which contains all five regular vowels and no other letters.

'Iouea' is a valid scientific genus name for a type of sea sponge, and it contains all five vowels (a, e, i, o, u) exactly once each, in order, with no other letters. While it's obscure, it's a legitimate taxonomic name. It's not a common English word but a scientific name, which fits the claim. Some sources mention 'eunoia' or 'facetious' as words containing all five vowels, but Iouea is indeed shorter and has them in alphabetical order.