It would be somewhat risky:
i5-2500 = 95W (and it will hit this with the demand a GTX1070 will put on it)
GTX 10570 = 150W
If you add in the fans, drives, etc you are looking at around 350W. That doesn't leave much left over, and I assume this power supply is somewhat older? They do age over time and become less capable due to capacitor fatigue.
I recommend either a lighter GPU, (i5-2500 is going to be limit your FPS), or upgrading to a 550W power supply to have some safety margin.
Also you need to consider things like plugging your phone into the computer to charge, or having wireless mice with charging stations.