We are shortly staying away for one night and leaving our 5 month old puppy with our parents. This is the first time she has been away from us and both we and our parents don't know what to expect. 
The puppy knows who our parents are as she sees them once twice a week.
Any advice on what to expect and how to deal with it.?

Well i dont have a puppy as yet but i have had the fully grown variety in the past so i hope this is of some help.
My dog used to love my mums slipper, so when we left her anywhere she took the slipper with her and she was happy, so i would suggest the same, something that smells of you, an old jumper or something like that, and take the puppy's own bed and toys so it seems as familiar as possible. Basically it may be similar to the puppies first night away from its mum, with you.

On the other hand as the puppy knows your parents it may well be fine :)

Hi

My girl Luna 11 month old labrador, spent an evening with my parents here the other day.
It was the first time she was away from me. My stepdad told me, that when he came and picked her up, she wouldn't walk without her lead on. The same happened in their garden, she was regarding her lead as a safety.

She didn't really relax - she was only there for a few hours, so maybe she wold've calmed down, if she was to stay all night.

Jeanette