is the speed of gravity waves infinity or do they move at the speed of
light? Is there any experimental data to support either answer. If it
is instantaneous could GW be used as the ultimate long range
communication tool?
If an object is 5000 light years away and then dissappears how can an
object 5000 years later be attracted to something that is not there if
GW is limited to the speed of light? Articles and researchers please.

General relativity predicts the existence of gravity waves that travel
at the speed of light. There is no direct experimental evidence for
this, since gravity waves have never been detected directly. The
radiative decay of the orbit of a binary pulsar was the first indirect
measurement of the effect of gravity waves, but did not establish a
velocity for the waves. General relativity is well supported by
experimental evidence and, so far as I know, any plausible theory of
gravitation predicts gravity waves that travel at the speed of light.

The second part of your question is about the speed of propagation of
gravitational fields, not of gravity waves. Again, however, they
propagate at the speed of light. If a massive object suddenly moves,
remote objects experience a force that points to the old position,
until the disturbance in the gravitational field reaches them,
traveling at the speed of light. Exactly the same is true for the
electric field of a charged particle.

"If an object is 5000 light years away and then dissappears how can an
object 5000 years later be attracted to something that is not there if
GW is limited to the speed of light?"

   Well, think upon this: If I shine an incredibly powerful flashlight
toward a planet 5,000 light-years distant, in 5,000 years observers on
that planet will see the light, even though the batteries ran dead
4,999.9 years earlier.