i5-3570k CPUs (LGA1155 socket)



No. The Z87 board is LGA1150, and the 3570K is LGA1155. Two different sockets with different amounts and placement of pins.
 
The most important thing in CPU/MOBO selection is compatibility. That CPU is NOT compatible with that Motherboard. Make sure that the Motherboard has a LGA1155 Socket to match your selected CPU so you don't ruin your CPU.
 
For a cpu to work in a mother board the motherboard must have the same lga socket as the cpu. Make sure you have it right you can usually see this in the specs of a motherboard on a website (Amazon, Newegg ect)
 
although the socket is different, it is designed for 3 gen CPUS (i3,i5,i7) but it needs to be exactly the same with your CPU