To be more specific what is your case? the motherboard can handle the graphics card having a x16 pci-e slot, what is your cpu? depending on the cpu, it can bottleneck the graphics card, sometimes does not worth adding a powerfull graphics card if your cpu can't handle fully its power.
If you give more specific information about your case i can tell if the graphics card will fit or not.
Well if you have an LGA 775 motherboard you will likely have a bottleneck with 570. I suggest something lower such as 460, this needs something like E7400 or better. If you tell me does it fit or not, measure your case, from the PCI-E slot to the where your side panel will go, and measure the distance from your PCI brackets to the HDD cages. Then compare the distances to the card you're going to buy. As for motherboard, you're fine as it has one PCI-E x16 slot.
And as I told you, if you don't have those high end LGA 775, you will likely to have a bottleneck with a 570. You go better if you get a 460. But before all, just provide me your system specification?