The GTX 295 is 10.4 inches long. Allow a little more for the power cables.
The ATI 5870 is 11 inches long. Allow a little more for the power cables.
You will need a pc case that is in excess of 20 inches in length from front to back. A length closer to 24 inches would be better. The case should also be at least 8 inches wide to accomodate a 160mm tall tower style cpu heatsink. The case will be quite a bit larger than the typical atx mid-tower case.
Here is a link to one example, the Coolermaster HAF 932:http://www.newegg.com/Product/Product.aspx?Item=N82E16811119160
I have that case. It is huge. Ventilation, airflow, and cooling are excellent. If you would like something different look for cases with similar dimensions.