I don't think you really mean any other way . . .

#!/usr/bin/env runhaskell
module Main
  where

import System (getArgs)
import qualified Data.ByteString.Lazy.Char8 as L

has_all_vowels :: L.ByteString -> Bool
has_all_vowels word =
  map (\pred -> pred word) predicates == [True,True,True,True,True]
  where
    predicates = (map (\c -> L.elem c) "aeiou")

words_with_all_vowels = filter has_all_vowels . L.lines

main :: IO ()
main = do
  [infile] <- getArgs
  contents <- L.readFile infile
  mapM_ L.putStrLn $ words_with_all_vowels contents

--
-- $ {time ~/vowels.hs /usr/share/dict/words} | wc -l
-- ~/vowels.hs /usr/share/dict/words  0.80s user 0.04s system 99% cpu 
+0.852 total
--    5942
--
[download]

Addendum: Mine doesn't handle AEIOU correctly, but then neither does the OP's.