my tv supports 4k@60hz via hdmi only and there's no DP. What should I do to reach this resolution with my NUC ?
Nothing. You can't get 2160p@60HZ via HDMI !
And even more, the new models with Skylake NUC6i5SYK/NUC6i5SYH will have the same HDMI 1.4 port no HDMI 2.0 so no 4K@60Hz !
Intel® NUC NUC5i5RYH DisplayPort and HDMI configurations feature the following:
• Two independent displays
• Single HDMI 1.4a with 1080P support
• Collage Display
• Single DisplayPort 1.2 with 4K support.
Please refer to table 6. Multiple Display Configuration Maximum Resolutions in the Technical Product Specification (TPS) https://downloadmirror.intel.com/24565/eng/NUC5i5RYB_NUC5i3RYB_TechProdSpec02.pdf on page 23 which states Intel® NUC5i5RYH supports Single display HDMI configuration 4096 x 2304 @ 24Hz Maximum.
As mentioned, Intel does not hide that fact from you. Moreover, future devices will not support HDMI 2.0, too.
If you'd still like to be able to watch videos in 4K (24p or 30p) on your TV without having to manually change the resolution, take note of a new feature in recent Kodi builds. The application automatically switches to 4K for videos with such high resolutions and back to 1080p after finishing the video.
Have you tried a mini display-port to HDMI adapter cable (rather than mini HDMI to HDMI)? I have my D54250WYKH connected to my AV amplifier/Samsung TV via the mini display-port to HDMI cable and everything works fine (only 1080p). This port may fix you problem of going to 4k @ 60Hz.