Hi there - I'm not hugely experienced, but my Harvey (10 weeks) did the same, 5:30am (yawn!) I just made a point to always tell him to get back in to bed - pointing to his bed whilst doing so. It took 5 or 6 goes on the first night/morning, and, now, after about 5 days, he goes back to bed as soon as I tell him to. In fact, last night, he slept from 11pm to 5:30am, woke me, I told him "bed" and he went back to sleep until 9am (a MASSIVE lay-in for me!
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I think it's all about consistency - and not talking too much when you do it, making sure you turn over and go back to sleep, so he knows it's not time yet...or, I might just have an extremely lazy puppy!
- I hope it works out for you
p.s. He sleeps in his pen, with a puppy pad at the mo, so can freely wee, although he's getting "dryer" through the night