as far i can see in the manual: http://support.dell.com/support/edoc...n/cs/cs_en.pdf
the Dell Inspiron 560 linup all has the same motherboard just with different CPU's. (so you can choose how much money to spend)
If the socket on the motherboard is the same as the CPU, it will most likely work. but it's not always the case.
Like the first lga-1155 motherboards did not support Ivy-bridge CPU's before a BIOS upgrade.
Your motherboard will be able to use all from the Pentium-4 lineup to the core-2-quad lineup, because the Dell Inspiron 560 model already have support for the core-2-Quad CPU's. i don't know about core-2-Extreme btw, but don't bother looking into that, those are very expensive.
My Dell Demension did not have support for a pentium D, because no Demension 5000'ens did have a Pentium D.
so Dell didn't make the support for it. (they did later on via a BIOS update)
The best demension 5000 had a 3,2ghz pentium 4 and mine had a 2,8 pentium 4.