You chose the i5 4570 which is not an unlocked processor(i.e. you can't overclock it) and a CPU cooler designed for overclocking.
Do you plan to overclock?
If yes, then go buy the i5 4570k.
If not, i would suggest using the stock Intel cooler.
Furthermore, if you REALLY want a custom cooler(even if you don't plan to overclock) you could get the Cooler Master Hyper 212 EVO(http://www.newegg.com/Product/Product.aspx?Item=N82E16835103099) which is cheaper and has a higher price/performance ratio(however it's not as powerful as your current choice).