“became the father of Shem, Ham, and Japheth.” Although Genesis 5:32 seems to say that all of Noah’s sons were born when he was 500 years old only the oldest son, Shem, was born at that time. This can be clearly seen by studying all the scriptures on the subject. Shem is said to be Japheth’s older brother in Genesis 10:21 (this is translated poorly in the KJV, which seems to say Japheth is older). Also, Ham is said to be the youngest son in Genesis 9:24, where the word “younger” is better translated as “youngest.”
The flood came when Noah was 600 (Gen. 7:11-12). Since Genesis 11:10 states that Shem was 100 years old two years after the flood, he would have to have been born when Noah was 502 years old.