Best Value, 2 Laptops

i7 over i5 in the same series is usually not worth it, especially within the ultra-book class of laptops. Marginal performance difference. Although another difference between the i5 and i7 versions is that the i7 version has discrete graphics. Again, may not be important for your usage.

What's your intended use? Office programs, browsing, videos?

$799 is a bit much for a notebook with a mechanical hard drive, though. How important to you is the quasi-crappy-tablet touch functionality?

None of that calls for particularly powerful hardware. I ask about the touch screen because if you take that out of the requirements list, you find cheaper, better laptops all over the place, like this one: LINK

Slightly thinner, lighter, cheaper, and faster (mainly due to the SSD). Fits your criteria for size and keyboard layout. Has a dedicated GPU, too, but that doesn't really matter. It's just a well-rounded machine.

If you still want something with a touch screen, I'd recommend either of these over the HPs, mostly because they come with SSDs, which will be more important than worrying about small differences in other hardware specs:
LINK
LINK

Did you intend to post a link? Or are you asking about the ASUS I linked above?

The biggest problem with the one you linked is the lack of SSD. That automatically makes it slower than every other laptop I linked regardless of whatever other hardware it has. If you'd like me to post my usual spiel about SSDs, I will.

The ASUS I suggested is thinner, lighter, has a better GPU, and an SSD plus the 1TB of storage. Only $60 more. If you're worried about 5th-gen vs 6th-gen CPU, don't be. Performance difference is negligible.