The vowels are A, E, I, O, and U.
Here's a breakdown:
* "The" has 1 vowel (E)
* "many" has 2 vowels (A, I)
* "vowels" has 3 vowels (O, E, U)
* "are" has 1 vowel (A)
* "in" has 1 vowel (I)
* "the" has 1 vowel (E)
* "following" has 3 vowels (O, I, I)
* "sentence" has 3 vowels (E, E, E)
* "and" has 1 vowel (A)
* "Samuel" has 2 vowels (A, U)
* "both" has 1 vowel (O)
* "had" has 1 vowel (A)
* "nightmares" has 3 vowels (I, A, E)
* "after" has 2 vowels (A, E)
* "seeing" has 2 vowels (E, E)
* "horror" has 2 vowels (O, O)
Adding all the vowels, we get 1 + 2 + 3 + 1 + 1 + 1 + 3 + 3 + 1 + 2 + 1 + 1 + 3 + 2 + 2 + 2 = 27 vowels.