This message was posted on behalf of Intel Corporation
Thank you for contacting Intel Communities.
The Intel® Core™ i5-2500K Processor is a quad-core processor (it has 4 physical cores) and does not have Hyper-Threading technology.
The HP link you provided shows information on a different processor, Intel® Core™ i7-3770 Processor. This processor has Intel® Hyper-Threading Technology. If Hyper-Threading technology is disabled, you will only see 4 cores in the device manager, and if Hyper-Threading technology is enabled, you will see 8 cores. The device manager will display the number of cores plus the number of threads (if there is Hyper-Threading and if it is enabled).
I hope this information helps.