Thanks for joining the Processor community.
Please bear in mind you own an Original Equipment Manufacturer (OEM) computer, therefore, this type of compatibility depends on the OEM.
Based on the computer specifications, it comes with an Intel 5500 chipset; please check the list of compatible processor for the chipset 5500.
If you noticed, the X5960 is not listed above. I recommend contacting Dell tech support for more information about processor upgrades: Chat Technical Support | Dell US