Pete (Ptss), i7, i5, and also i3 refer to different series of Intel CPU chips. Various versions of each series have existed since around 2010 for laptop applications, and since slightly before that for desktop applications. Each series has evolved through several progressively more powerful generations during those years, the latest generation being referred to as "Skylake," or as "6th generation core processors." (I believe, though, that large scale introduction of Skylake-based laptops may still be a few months off).
While within each of the three series a number of different speed ratings and other parameter differences exist, as a general rule of thumb the i7's tend to be more powerful than the i5's, which in turn tend to be more powerful than the i3's. Although in general faster speeds and greater computing power correspond (within a given generation) to more heat being generated, which can rule out the use of many high powered CPUs in a small laptop, and to shorter battery run-times.
Regarding the issues Steakster reported in his last post, my guess is that the problems are driver-related. It's not uncommon for HP and other manufacturers to not release driver updates that would make older computers compatible with new versions of Windows. As well as for the drivers that are built into a new version of Windows to not be compatible with older computers. In the case of laptops, I've found both situations to be particularly true when it comes to graphics/video drivers.
Regards,
-- Al
