Your sentence is almost perfect! Here's the original sentence:
Black swans start off as grey and turn black as they grow.
This sentence is grammatically correct. It means that black swans are grey when they are young and become black as they get older.
If you'd like, you can add a little more explanation for a 5-year-old, like this:
Black swans are grey babies, but when they grow up, they turn black.
This version uses simpler words that are easier for young children to understand.