Hi littleweed, you don't say how old the little one is or if the cot in your room or a seperate one?
Grandson was often a pain in the butt if he woke up when his cot was still in our room. No matter what we tried, he wouldn't settle, wanted to play, cuddle, etc.
Once we moved him into his own room, it wasn't a problem. He initially went through a phase of waking up early - but, if he was happy, I'd leave him and more often than not, he'd go back to sleep. Sometimes, when I knew that he was wide awake - I'd throw toys in the cot. But whatever I did, I always put him to bed and got him up at a consistent time.
He now goes to bed at 6 and stays in until around 8 the following morning. I usually hear him at around 7.00-7.30 and he can hear me moving around, etc. He often shouts hello gamma (so sweet), but now he plays in his cot quite happily and patiently whilst I do the shower thing and have a quick tidy up or whatever.
To be honest, if it was mine waking at 5.30, I'd want him to go back to sleep, so if he's happy, I'd leave him, wouldn't acknowledge him or let him know I was awake. He'll eventually get the message and learn that it's still bedtime.
Good luck.