--But, do you know it will take 5000 years to get there from here? A heckuva lot longer than that. IIRC, the center of the Milky Way is about 40,000 light years from Earth. About 250,000,000 years away at the speed of a Voyager type probe.
They have to move the probe a lot faster than the Voyagers. In 1/4 billion years the probe would probably simply evaporate before it got there.