I wouldn't do it. As a teacher of kids this age I think there are too many variables and unless it is an emergency I would leave it a few years. Even confident happy 5 yo's can fall in a heap on such a long flight. I flew to Perth a couple of years ago and was seated next to an unaccompanied kid. He was about 10 I reckon. Once the hosties realised I was chatting to him and playing squares and 0-X's with him they totally ignored him. It was quite a boring flight for me as I'd have loved to have read a book instead of entertaining that kid!
He was a lovely boy, very polite etc. but it was not my perfect flight and I am unsure if all passengers in my position would have been as kind to him.
There might be a cheaper way for you which was a system a friend's parents used to shuttle their children between Brissy and NZ.
They found responsible Uni students who wanted a cheap holiday in the destination and offered to pay half their fare if they travelled with the kids......cheaper than two parents going two ways and a good carer on location should anything go wrong.
There were good candidates tripping over themselves to "help out" and the kids got to know them before hand as babysitters..........
Just a thought.