No he’s not. He’s 25 in the very first chapter. In this latest chapter he’s 20. He runs way for 5 years. At the start of the flashbacks he’s 15, then the prince left him alone for 5 years until now so 20 and then he ran way for another 5 years so 25. It’s mentioned in the novel. Right now he’s 20 years.
In the novel, Mok-young (the prince) refers to him as “that child” for some reason, I’m not sure, but Dam is 25 in chapter 1. When they first met Dam was 15 and I believe Mok-young is 3 years older than him, it’s mentioned he was around 23 years when Dam was 20 years. Anyways, after the execution of the Royal Pharmacy chief, the next chapter mentions there was a 5 year time skip (chapter 11) and this latest chapter mentions the 5 year time skip that Mok-young ignored Dam until now. So Dam is 100% 20 years old and I believe Mok-young is 23 years. Later, after the flashbacks and we are in present time, 5 years will have passed.

So you're saying that in the novel he's still minor ?