How long does it take for National Express coaches to get from London Victoria station to Luton Airport on Sundays' early mornings (about 5 am)?
At that time in the morning The journey usually takes just over an hour.
If you look at the time tables you will see that as the day progresses national express allow extra time for the service to run.
Depending on where you are in London you might also want to consider two other options. National express and easy bus offer a joint service to Luton airport from Baker Street and other stops in London. Which might actually be on the same bus that picks up at Victoria However prices can be cheaper. Check the prices on the easybus website
The other option from London to Luton airport is by rail, with First Capital connect services from London bridge, blackfriars, kings cross st pancreas. It's worth checking however as this summer there are a number of weekends when this line is closed for Maintainance