age 5 vs the age of 5

Yes.

Thanks, engineer.

Which is the better version?

There are lots of ways to write this sentence depending on what you are doing. For example, age can be assumed in context, so you could be concise and write:

"Annabel, 23, graduated from Harvard University last year with a degree in Computer Science. She’s been an avid dancer since she was a child, and started ballet lessons at five."

I personally like "the age of 5" better. Whether that is the better version is probably up to the reader.

Many thanks, engineer!