Can anyone link me to the adapter/connecter i need?
One of these is usually included in the box with your graphics card.
Edit: Some guy posted: Your current PSU's 12 volt rail is only at 18 Amps, it doesn't have enough power to supply the GPU and processor together.
Is that true ^
Yes, this is true. You will need a new PSU. The one linked above should be adequate.
*Im excited. Switching from Radeon HD5550 to 6870... Should I expect a huge diffrence in FPS in games?
A huge difference? Maybe not huge, but you should certainly see a very noticeable improvement. Going with the 7850 as suggested would further increase that.