Simple math on the age of mankind?

As per US Census Bureau, as of now, there are 6,775,377,28 people in the world. Assume we grew at the rate of 0.5% every year, there would have been only 5 people before 4217 years. Does it sound like a reasonable number? Is there anyway, we can get some material which has some proof to believe that mankind existed before 'y' years.