All PCIE-E x16 cards are backwards compatible. Chipset does not come into it. For example, you could run a PCI-E x 3.0 GPU in your slot and it will work. They simply won't work at "full" capabilities. They will be limited to the motherboards slot speed.
If a 550ti/560ti can physically can fit into your case - then yes you can run one (provided you use the Silverstone PSU. The dell generic just isn't up to the job).
My Computer
Computer type
PC/Desktop
Computer Manufacturer/Model Number
Systems by SmartEyeball
OS
8 Pro x64
CPU
i7 3770K 4.6GHz
Motherboard
ASUS P8Z77 WS
Memory
16GB G.Skill Trident X 2666mhz
Graphics Card(s)
x2 EVGA 780 Ti Superclocked SLI
Sound Card
SB X-FI Surround 5.1 PRO USB / ATH-AD900 Headphones
Monitor(s) Displays
x3 Dell U2410 / 58" Samsung
Screen Resolution
5760*1200/ 1920*1200
Hard Drives
2x Intel 520 240GB (RAID 0) * 2x WD Caviar Blacks 2TB (RAID 0) * 2TB WD Caviar Black * Sony Optirac DVD
Thermaltake Theron (Highly Recommended) + Razer Imperator
Antivirus
MSE
Browser
IE, FF, WaterFox
Other Info
GT Extreme V2 Sim Racing Cockpit + 40" LCD and K/B Mouse stand ▼
Fanatec CSR Elite Wheel + Clubsport V1 Pedals + CSR shifter/7G-H ▼Saitek X52 Pro ▼ TrackIR 5 Pro
Buttkicker v2 Seat Rumbler with Dedicated 5.1 and Sub Woofer attached to frame ▼
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Bloody Big Grin