Hopefully some "painters" will chime in for the details. Here is some general info regarding paint codes and paint mixing.
When you pick a paint color, that color is a combination of several colors mixed together. So if you pick color "x", the paint shop looks up the formula in a book. It might be 2% "y", then 8% of "z" etc.
With that being said, you use that exact formula with a different brand and the color can be a completely different shade or maybe not even close.
So paint code 5706 is most likely going to look different with each brand of paint.
I would recommend first decide on a painter / paint shop. Then see what brand of paint they like to use, stand behind etc. If its not a brand you want to use and they won't spray your choice, then move on to the next shop. Once you find your painter and the paint product, then go for the color match of your choice. Nothing beats personal recommendations from other 356 owners in your area.