Question about how fast dragons age

So I haven't even finished the first book yet (seen the other thing) but I'm decently into F&B and got to an illustration of Vermithor with Jaehaerys and Rogar. Correct me if I'm wrong but Vermithor is 15 years old at this point and still growing right? Drogon in the books must be at most 2 years old at this point. I imagine Drogon will be coming to Westeros soon so he'll be what, like 3-5 years old? Balerion was 120 years old during the Aegon's invasion. Do dragon's reach max size after 5 years or is Drogon going to be pathetic when he gets here?