Rev. James Smith Bush (June 15, 1825 – November 11, 1889) was an American attorney, Episcopal priest, religious writer, and an ancestor of the Bush political family. He was the father of business magnate Samuel Prescott Bush, grandfather of former US Senator Prescott Bush, great-grandfather of former US President George H. W. Bush and great-great-grandfather of former US President George W. Bush.
Samuel Prescott Bush is the great-great-great-great-grandfather of George Bush.
The son of someone's great-great or someone's great-great-great grandfather cannot also be their great-great-great-great-grandfather. I think the multitude of "greats" challenged the system.