Golden Ages started by Great People don't count as far as I can tell. Do all golden ages have to be from Happiness? What about from say Reformation or Rationalism, the cultural GAs?
The achievement will only trigger on 'natural' golden ages which come from citizen happiness.
Any of the ages which you can trigger yourself, via social policy or great people don't count.
If you are trying to nail the badges, the best solution is to focus on happiness improvements, and grab Meritocracy and Organized Religion.
After trying a bunch of times to get this achievement, i realized this :
With Gods and Kings expansion golden ages don't occur the same way, comparing with the original game.
In the original Civ V, you have to stack 500 happiness, then 750, 1000, 1250, 1500 etc. In Gods and Kings, it's 500 and doesn't increase. I think that's the reason why i couldn't get the achievement.
I simply disabled Gods and Kings in the DLC in-game menu, ran a settler difficulty game, and earned (at last) the achievement by starting 5 "happiness golden ages", like stated above.
Hope this helps.
PS: For I don't have Brave New World expansion pack, i cannot tell if it blocks the achievement, or not. If it does, i gess disabling it should fix the problem, like it did for me with G&K.