How Ati Radeon HD 5970's mem bandwidth is calculated?

The memory has QDR (Quad Data Rate) 4 read/write per clock cycle, that is x4 not x2.

difference between QDR and DDR2?  

DDR = double data rate x4 operations per clock
QDR = quad data rate x2 operations per clock (you multiplied by 2, not 4)

GDDR5 is sorta like QDR but not really. It is more like 2xDDR.

DDR2 and DDR3 is not DDRx2 or DDRx3. It is DDR revivsion 2 and revision 3. Both are double data rate. GDDR is something a bit different. You can google it and read pages on it if you want.