I have got up at 5 a.m. today.
i got at 5.00am .
i got up at 5.00 am
Bad. Don't use present perfect with a definite time. "I got up at 5am today" or "I have got up" (or even "I have gotten up")
But what if the 'today' has not ended yet?
*facepalm* Obviously 'today' has not ended.
because i have got up at 5 a.m today is not a good english
This is a statement of fact regarding a specified and defined time. The past simple tense should be used.