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As "got" is the past participle of "get" in British English, I would say it is correct in British English. In American English it would not be correct. In American English it would have to be "gotten".
Even if we remove the modifier: Often, it will still be wrong.
It is correct (in UK english). Ignoring preferences to punctuation, to say "I have often risen at 5am" is surely correct. (The various translations of the opening words of a la recherche de temps perdu could give a guide here). Assuming that "got up" is an acceptable alternative to "risen", there is nothing wrong here.
"got" isn't in the correct tense, therefore it's not perfectly comparable to "risen"
hi what's up
I used to get up at 5 a.m
I usually got up at 5 a.m