Both are correct but have slightly different meanings. " I woke up at 5:30 am" means that you woke up at 5:30 am exactly, but "I got up by 5:30 am"means you were awake before 5:30 but we are not saying exactly what time.

They are completely different. 'Woke up' means you stopped sleeping and opened your eyes. 'Got up' means you left your bed. First you wake up. Then you get up. Simple as that.

I think that the correct form is i wake up at..... If you want speak in present tense

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