Apparently in the books, the age difference between the king and Alicent is much less:
https://www.avclub.com/ok-so-just-ho...gon-1849467592
They never really say how old the king is (although he looks quite old). His brother looks a lot younger than him, and they have the same two parents. I always assumed they made the kind looks a lot older than he was, as he was going through poor health from that mystery disease that is stopping his wounds from healing.