H55 is for the integtated graphics on every ( I think ) i5 EXCEPT the i5 750.....the 750 does not have the onboard graphics.
The main difference between X58, P55 and H55 is the number of PCI Express lanes and the speed they run at.
As long as you only want to run 1 graphics card H55 should be fine for you but....the H55 was really designed for onboard graphics and every other i5 EXCEPT the i5 750 because they all have on chip graphics support.
This explains better http://ixbtlabs.com/articles3/mainboard/i55h-57h-chipsets-p1.html
Hope that helps.