At Shul, I heard repeatedly that the Jewish people were 4000 years old and I had always thought that it was over 5000 years. I know that this is 5765 so how could it only be 4000? Thank you

The world was created 5766 year ago. Abraham, son of Terach father of Isaac, AKA "the first Jew", was born 1948 years later. It is therefore a common saying that the Jews are around for almost 4000 years.