Can the Mushkin Joule 700W run two Sapphire Radeon HD 5870s Vapor-X Edition on crossfire with an AMD Phenom 9950 BE and couple of Hard Drives ?
That's a good question, and something I think you'll be happy to know the answer to - yes, you should be fine. There's two 6-pin PCI-e power connectors required per GPU, with 75W through each connector gives us 300W. The board itself will provide 75W to the GPUs, so you're getting close to 450W there.
The rest of the system will use around 100-150W of power, so you should be fine. I don't know if you've already go one Sapphire Radeon HD 5870 Vapor-X GPU and are looking to get another, if this is the case, get yourself a HD 7770 and replace the 5870.
Your Mushkin Joule 700W PSU should be fine for either setup.
You can always CrossFire those GPUs down the track and they'll use less power, too.