As a father, I'd like to put in my 2 cents if I may.
This is a really interesting discussion, because while certain aspects of Aquaria (or should I say some of Naija's forms) are fit for 5-y-olds, others could even be considered X-rated by some. There is not much gore or visual violence, but the game is in fact dark and has parts that need to be explained. I'd say that the key word here is "supervision".
I play the game with my 3-year-old daughter on my lap. She's too young to actually control Naija, so she tells me where to go and I do it. She calls the 1st form "Good" and the 2nd "Bad" and she wants me to keep swapping, telling me to "be good" or "be bad". To be honest, I thought the Energy Form was pretty evil myself after swimming around singing for the first couple of hours of gameplay. So that's one thing. Plus of course there's the 3rd and 7th forms too.
The darker parts of the game (the Abyss, the Cathedral, the Body) and many creepy areas are certainly things I wouldn't like her to see alone, mainly because she might be scared. But then again she's 3. I don't know what I'd be like if she was 13. What worries me most though is the whole role of the Creator. ..
*****SPOILER FOLLOWS****
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...once you start deciphering the Aquascript there's plenty of pretty gloomy (to say the least) messages scrawled all over the place, as well as some bleak images of the Creator. The whole idea that your God is evil and must be destroyed is a questionable one, and certainly one that many parents would object to, especially if they are religious. I can imagine several who'd rather not let their kids have that sort of influence.
So, to sum up, even though the game does not really have any extreme images, and even though on average it mostly involves swimming about in pretty waters, there are elements that certain parents could find disturbing. My advice would be to finish it on your own first and then decide whether you want your kids to play it. Personally, I play certain areas with my daughter and others on my own when she's away. And I certainly don't want her in the final battle (mainly out of fear she might accidentally press some key).
