Which part of speech is 'all' in the sentence?

Interesting question. Quirk et al list it as a postposed predeterrminer or pronoun here. However, they say that when in this structure 'all' takes the position of a medial adverb:

They all won their matches.
We were all fast asleep.
The villages have all been destroyed.

Hi Mister Micawber,
Thank you for your reply and examples.
Is it a book 'Quirk et al list'?

So 'all' is an adverb, in your examples it modifies the verbs, doesn't it?
Does in mine modify the adjective 'five'? They are all five years old.
Is there a synonym for 'all' here, or it is just used for

Quirk, Greenbaum, Leech & Svartvik, A Comprehensive Grammar of the English Language.

No, 'all' is not an adverb: it is determiner that takes the same location as an adverb in such sentences when it postmodifies. At least, that is what the book says.

They are all five years old. Is there a synonym for 'all' here, or it is just used for emphasis?-- For emphas

Hi Mister Micawber,
Thank you very much for your reply.
It has to be a very good grammar book.

Best,
TS

"All" in this sentence is a postposed predeterminer because it is modifying the subject, "they." It qualifies "they" but occurs after the verb instead of before the noun it modifies. You can imagine this sentence as equivalent to "All of them are five years old."

In other words, it is an adjective being used in an adverb's location in the sentence.