
Hi moonyrocks
you don't say how old your puppy is or how long you have had her :) If she is a very recent addition, it may be that her body clock is kicking in at 5-00am because that is the time she was used to being let out (or possibly fed) by the breeder in which case over a couple of weeks she will have slotted better into your own routine.
In the meantime it sounds as though when you get up to her you're actually making things a little too interesting - for example,
>Ive tried showing her her water
Does your puppy always have access to fresh water, even overnight? If not, perhaps she's thirsty which would be resolved by leaving a bowl of water for her to take from anytime. If she already has easy access to water, then there's no need to "show her" - by doing so you're interacting with her which will wake her up more and cause her to fret more when left again.
Re giving a snack - again, counter productive to her settling down :)
>letting her out in the garden for a bit of a run
Better to clip a lead on, walk out to the garden with her, let her relieve herself without a huge fuss and quietly return her to her sleeping quarters. Don't encourage excitement :)
Re house training in general, I find it better to pre-empt the time my pups will need to toilet overnight so wake them and take them out as above then return them to their bed while still sleepy. Even though this will involve breaking your own nights sleep it wont go on for too long and will speed up the house training as well as help form her personal "clock" towards a time that will be more family friendly :)
HTH, regards Teri