As far as we know, it is true. Our earliest sources of Mozart's work is a notebook used by the Mozart family written between 1759 and 1764, so when Mozart was between 3 and 8. Interspersed in this book are little pieces attributed to Mozart, the earliest of which are in the hand of his father, which suggests Mozart played them and his father wrote them down. The earliest of these you can see (and hear) in this video. The piece bears the marking "Des Wolfgangerl Compositiones in ersten 3 Monaten nach seinem 5ten Jahre," indicating that these were composed when Wolfgang was roughly 5 years and 3 months old.

So the earliest documented piece of music we have suggests that Mozart was composing when he was 5, at least. There are somewhat apocraphal stories of Mozart composing when he was four, using his own idiosyncratic way of notating compositions. I am away from my home library for the holidays right now, so I can't verify using my biographies what the source for this is, and internet sources are not helping me very much, just relating the anecdote without a source, or pointing to a biography without a page number (grrrr). In any case, I can't evaluate this claim at the moment. But we can at least say with relative security that Mozart was composing by the time he was 5 years and 3 months old. Hopefully this weekend I can figure out exactly where this claim that Mozart was composing a year before his first documented piece comes from!