Depends which model, and whether you are talking about physcial cores or virtual cores, for example a processor can have two physical cores and two virtual cores and still be branded a "quad core"
Apart from the bottom of the range i5 650, the rest are sold as "quad cores" although they don't have four physical cores.
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All shipping Core i7 processors have four cores but they each run two threads at a time so in a sense it's 8. Your computer will even recognize it as 8 cores.
Intel i5 processors have 2 cores, and 4 processing threads.
Source: http://www.intel.com/content/www/us/en/processor-comparison/compare-intel-processors.html
It has 2 cores with 32nm fabrication...some what equalent to core 2 duo when you consider cores number but performance is far more superior in i3
There have been dual-core and quad-core processors in the Intel i5 family, so they can have either 2 or 4 cores.