"Mix of sizes, 2k, 3k and 5k"
You would need Max GPU memory to play back that high resolution material consistent flawless.
How much on dedicated Memory does the Nvidia GTX580 have?
Later, I searched at new egg, they had GTX580s with choice of either
1536MB or 3GB.
You may need the 3gb model to get MPE Hardware acceleration correctly with 3k and 5k material.