Notes on your definition:
You could exclude apple as an outlier by changing "in the next few years" to "in the first few years".
Concerning the significance of growing by a large factor; you might want to consider changing the absolute number to a recurring value. 500 users in the first year which turn into 5000 after five years is hardly significant. 500*5^5 = 1.562.500 is starting to feel significant. The actual growth factor per year might need to be altered.
"repeatedly grow by a large factor (5x or more)"
Ambitions and plans could be refactored to "aims"; if you're aiming to do something you probably have the ambition and you sure as hell need to have some plans or your ambitions won't go anywhere. Although it might be better to explicitly mention ambitions and plans.
In conclusion, my refactored definition would be
"A startup is a business which aims to repeatedly grow by a large factor (5x or more) in the first few (1-5) years.