I am just wondering what the norm is - should/would you fly at 5/6 weeks pregnant?
Give your GP a call and check, doubt there will be any problem with it.
Just wrote a reply but vanished!
I'd ring GP/hospital but should be fine if short haul and you've had no previous problems (miscarriage/bleeds etc).
There are lots of similar posts if you do search.
Keep hydrated, avoid tea/coffee/alcohol that day.
Try to walk around plane or follow exercises in the seat pocket on the plane (moving feet and legs etc). Baby is tiny at that stage, but just bear in mind that if you suffer from morning sickness already you might find it tough.