Are there any words which use all five vowels next to each other?
There aren't any such words in common use, though the 20-volume historical Oxford English Dictionary does contain the word Rousseauian meaning 'relating to the French philosopher Jean-Jacques Rousseau or his views on religion, politics, education, etc.'.
The more familiar words queuing/queueing contain clusters of vowels but there's no letter 'a' among them.
Some words which come from Greek also contain several vowels strung together, for example pharmacopoeia or onomatopoeic, but none contain all five vowels with no consonants in between.
See other Vocabulary Questions.
Take a look at: Do any words have all five vowels in order?