It certainly will. AMD HD 5 series and 6 series can properly be seated at PCI Express 2.1 x16 bus interface. Of course the latter has better memory bandwidth at 73.6 GB/s (maximum).
If you have already had the latest drivers and Catalyst Control Center installed, then just replace the card and run.
Computer type PC/Desktop System Manufacturer/Model Number Self built system OS Windows 7 Ultimate x64 CPU CORE i5 Motherboard Intel DH55PJ Memory 4GB Graphics Card ATI HD 4650 Sound Card Realtek HD Integrated Monitor(s) Displays LG Flatron L1742S; LG Flatron 19"; Toshiba 32" Screen Resolution 1280 x 1024; 1366 x 768
Keyboard Logitech Wireless Mouse Logitech Wireless PSU Power Case Simbadda Cooling Conventional Hard Drives Seagate Barracuda 500 GB
WDC 1 TB Internet Speed 256Kbps Other Info External HDD Transcend 500GB
Dial Up Modem Huawei
Home-made Home Theater
Laptop ASUS K42F, Core i3, 4GB memory, 320GB HDD.
LAptop Fujitsu LH531, Core i3, 4GB Memory, 500 GB HDD, Nvidia VGA