Is there any evidence from observational cosmology to say Dark Energy dominated era begins 5 billion years ago People say that Dark Energy Dominated era begin 5 billion years ago. Do we have evidence for that from observations 
 A: Last I heard there was no direct experimental evidence to pinpoint the onset of the accelerated expansion. Evidence for this will probably come from very precise measurements of the Sn1a luminosities, but at the moment the data isn't precise enough.
However the indirect evidence is compelling. We have established that general relativity gives a good description of the universe, and the CMB measurements tell us that the assumptions we use to construct the FLRW metric are (reasonably) reliable. Finally we know from the Sn1a and later the Planck CM measurements that dark energy/cosmological constant exists, and we have measurements of the various densities of baryonic matter, dark matter and dark energy.
From the data we have it is easy to calculate the scale factor as a function of time, and in fact I do just this in How does the Hubble parameter change with the age of the universe?. It just remains to determine the point of inflection in the scale factor vs time curve, and this gives you the 5 billion years or so ago.
