For the Sapphiere HD 5870 a 500Watt PSU is Min requirement and 600Watt is recommended.
The HEC R500 is PCI-E compatible so it should work fine.

I called the supplier , they say it's fine too ! Thanks ! :)

it should be alright, but I wouldn't but too much more on there. Idle it'll definitely be ok, but you'll be hitting close to the max output when you're maxing out CPU and GPU, and some PSUs really don't like being pushed to their limits; I used to run 2 8800GTS cards in SLI with some old hardware, I had a 600w power supply. Eventually, the PSU capacitors melted and started the PSu on fire while I was sleeping, not cool.

good thing it did not take your house along with it .

I hope my HAF 932 4 huge fans won't be a problem too..

DO you happen to know anybody who has a UPS? ( Uninterruptable power supply)? This can tell you what your computer is drawing (Unless it's a really cheap one) which is how I figure out what mine draws idle or during load.