the h87 is a whole different chipset, it will not do all the work the z87 motherboard does, the biggest one is overclocking, the h87 cant do overclocking but the z87 can, if you're not going to overclock just get a h87 and a i5 4570.
Along with what everyone else said, intel likes to reserve the 'z' for chipsets that have options for overclocking, whereas the 'h' is the same thing without the overclocking tools
So basically want to overclock? go i5 4670k/i7 4770k z87 mobo
Don't want to overclock? go any other i5 or i7 that doesn't have a k h87 mobo
the h87 is a whole different chipset, it will not do all the work the z87 motherboard does, the biggest one is overclocking, the h87 cant do overclocking but the z87 can, if you're not going to overclock just get a h87 and a i5 4570.