Hey there, twitch. De-lurking for a bit to ask a question about your mounting method.
First, some background: a few months ago, I upgraded my system to a new E3 1240 v5 Xeon (that's the newest Skylake E3) using a Kotetsu for cooling. Included in the Kotetsu's various bits of mounting hardware was an extra packet with a pair of spacing washers and special instructions for mounting on a socket 1151 system. Because of the widely reported
Skylake damage caused by overly tight installations of certain HSFs, the Kotetsu included, this was Scythe's solution. The extra spacing reduced the mating force, protecting our expensive processors.
The problem, at least with my Xeon, was that it was
too much spacing. With the washers installed as directed, the Kotetsu was so loosely coupled that it would wiggle when I touched it. Even though the mounting screws were bottomed out, I could twist it back and forth a few degrees with no noticeable effort. It was so loose that the Ceramique 2 TIM I used to mount it acted as a lubricant instead of a thermal conductor.
Though this was my first experience with an after-market HSF, I knew they should clamp more than hard enough to stay put. So I remounted it without the extra washers, taking care not to tighten it too much, for a guesstimated "too much." I'm not even sure I got the screws on both sides tightened evenly, but it works great.
I don't know if there are any differences in the substrate or heat spreader between the Skylake E3 and i5/i7 chips, but I wouldn't expect any. Based on the amount/pattern of TIM on your heat sink and processor, it looks to my inexpert eye like you didn't have nearly enough contact pressure. So, my question is this: did you use the extra washers for socket 1151 processors? Because that may be the problem.
If you're worried about trying the mount without the extra spacers and the possibility of damaging your costly equipment, as I was, you may take some comfort in knowing that
Intel's HSF mounting guidelines supposedly allow for up to 50 pounds (!) of force between the HSF and processor (the first paragraph in the link).
As I noted above, the Kotetsu does very well in my system, a Xeon/Kotetsu in a Fractal Design Define R4, and my Xeon and your i5 have identical stock clock speeds.