score:3
Take a taxi to the nearest MTR Airport Express train station, which would be Tsing Yi or Kowloon. Then take the train. It takes 24 minutes to get to the airport, and service starts at 5:54. The fare is $60 (HKD) from Tsing Yi and $90 (HKD) from Kowloon.
There are many buses that also go to the airport. You can find a full listing of them here.
Upvote:3
Your time frame precludes much, if not all, travel on the MTR, as you probably know. Train service starts a few minutes before 6:00.
The easiest way to get there is to just take a taxi. It should cost around 350 HKD. Not cheap, but quick and simple.
You could also take a bus. Not sure where exactly you are - Yuen Long is big area - but you most likely want the E34 A or B. Both go from Yuen Long to the airport and start running about 5:10. Travel time will be 60-90 minutes. The fare will be less than 20 HKD. You can plan your bus route in detail by using the official HK public transit planner. Be aware that if you have large or a lot of luggage, you may not be allowed to board the bus.