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So the schwa could adopt any of the 5 sounds of the vowels, right?
No. You may have misunderstood. (Or maybe you've written something there that isn't exactly what you mean.)
There are 5 vowel graphs (vowel letters) - six if you count 'y', but 14 vowel sounds.
The schwa can have any sound similar to the i, the u, or the oo as described above, but not other sounds. So no, the schwa cannot adopt (or take on) the sound of any vowel.

But any of the vowel graphs ("a, e, i, o, u, y") can be pronounced as a schwa in an unstressed syllable. Yes, that's true, if that's what you mean.