the fact that people are taught in school that english has five vowels is kind of ridiculous
we have (in general american):
- æ in cat
- ɑ in palm
- ɔ in thought
- ɪ in kit
- ε in dress
- ʌ in strut
- ʊ in foot
- i in fleece
- u in goose
- ə in comma (second vowel)
and that's just the monophthongs
-F
if you include diphthongs too, we can add
- eɪ in face
- oʊ in goat
- aɪ in price
- ɔɪ in choice
- aʊ in mouth
and that's just general american
other dialects can have additional vowels or different realizations of the same diphthongs (like ei instead of eɪ, for instance)
received pronunciation has interesting diphthongs like eə and ɪə as a result of being non-rhotic, and some triphthongs too
-F