Emmagee, oh yes, been there. 5.00 am is a truly horrible hour to have to start your day. May, June and July are the worst months, I find, for early wakings up. All that tempting sun peeping through the curtains. I've grown to accept that my sons will wake up with the dawn chorus every now and again, as I do, but what you seem to be witnessing is a developing habit. Not good, is it?
I've always tried to make the bedroom as dark as possible - I second Bugsey's black out curtain suggestion. Also think where you put the cot or bed. Not too near, or in view of the window. And possibly try this together with the bore-them-back-to-sleep-tactic, by taking too-interesting toys out of the bedroom, and tiding other toys away.
I've definitely found that tiring them out works wonders. A good long stint in the park, late afternoon should do it. At least the long light evenings give more tiring out possibilities.
As a last resort, I find that taking my early waking toddler downstairs and letting him play quietly with his cars for 40 minutes can do the trick. I just lay on the sofa, keeping a bleary eye on him with minimum interaction or stimulation - easy to do at that time in the morning. After a while I say 'bed time now' firmly carry him upstairs and go through a mini bedtime routine (nappy, drink etc) finishing with the set lullaby. Then leave him in his room, usually a bit of grumbing and crying, then zonk. About a 70% success rate with this! so worth keeping up my sleeve for one-offs.
Hope it gets better for you.