My pet wakes me up every morning at 6:00 to go outside. When I stumble back into bed for a few more minutes' sleep, he allows me to snooze off---just to wake me up 20 minutes later. After I reluctantly stretch and make a cup of coffee, guess what he does? Yeah, he goes back to sleep! Now, I love my guy, but disturbed sleep is making me a little grumpy. Full disclosure makes me tell you that my pet is a dog. But cats, if anything, can be much worse. If you love one of these infuriating creatures that rouse you out of bed at some ungodly hour, you know what I mean!
Cats are each different and their perceived needs are just as different. How Fluffy wakes you up is completely and entirely all her own method. I once had a cat that would climb up a rug that was hung on the wall behind my bed. My "alarm" went off when she launched herself out into space and landed on my snoozing, hapless, and unconscious body. Every day. So what's a sleep-deprived body to do?
Your cat may be waking you on purpose---because she desperately needs her water changed and three bits of kibble or she will surely die---but she also may be waking you up because she is awake. Before you can figure out how to get her to let you sleep, you need to understand why she isn't.
Nature structured our kitties to wake up early to hunt for food, so very early morning is likely when she wants to eat.. If she absolutely, positively, must be fed at 5:00 am, getting an automatic food dispenser may be all you need to do. Other needs may be a clean litter box, fresh water, or maybe she's lonely. Perhaps her bed gets too much light or is set in a drafty spot. The thing is, cats are seriously awesome trainers. If you got up even once to feed her, she figures she has you trained and all she has to do is remind you of your training. Her "intermittent reinforcement training method" means she believes most of the time, you'll do exactly what she wants you to do. All she has to do is remind you until you do!
Cats are naturally nocturnal, so if she's awake during the night, prowling and knocking things off a shelf (which for some reason is the most industrious thing she does) and making noise you simply can't sleep through, she's just being a cat. (My daughter has three cats. One of them has learned how to open dresser drawers and unpack all her underwear. Since it happens when nobody's home, no one knows for sure which cat it is. And they sure won't tell!) Making sure she has plenty of stimulation during the day may help even out her own sleep cycle. Households who have kids rarely have "early morning cat syndrome."
Putting her as far away from you as possible during the night and keeping your door closed might help. Finally, hiring someone to come sit and play with her during the day might be necessary, too. Unfortunately, cats are not easily trained out of their feline natures. But oh, those purrs and bumps of the head are so, so worth it!