When you look at a galaxy from 5 billion years ago, you're not looking at it as it was including the light shift. The red-shift they're talking about is not from the initial difference in velocity, it's from the wave length being stretched by the expansion of space as the light travels.
For example, the wikipedia article about the accelerating expansion [1] mentions things like:
> the distance-redshift relation deviates from linearity, and this deviation depends on how the expansion rate has changed over time
If the universe decided to suddenly increase in size by 1% over the next hour, all the already-travelling light would arrive with a 1% larger wavelength. If it had suddenly increased in size by 1% a billion years ago, the already-travelling light would get just that 1% larger wavelength but also 1% more travel time for stretching out to occur over. So if you have an independent way of determining distance... a lot of information falls out of that red-shift-vs-distance plot.