Q: WHAT YEAR WAS SHEM BORN?
A: IT DEPENDS WHAT CALENDAR YOU ARE USING!
On the Gregorian calendar (the one you might have on your wall) the year was 2483 BC.
On the Hebrew calendar, sometimes called the biblical calendar, the year was 1564 AM.
Genesis 5:32 New King James Version (NKJV)
32 And Noah was five hundred years old, and Noah begot Shem, Ham, and Japheth.