[BScout]

I know other studios that are struggling with 5k screens over HDMI and Pro Tools (mostly GUI lag not crashing)

I have one 4k and one 2560x1440 on my system and the system runs perfectly (Mac 5,1) -- both at full resolution. 2560x1440 via DVI-DL and 4k via displayPort to HDMI (this needs SwitchResX to get the resolution/timings right.)

I do know on the Mac 6,1, not all thunderbolt ports are the same. This happens with a studio I work at with 3 screens and they have to be on particular ports or there are problems (I believe one of the screens even has to be attached to the Sonnet chassis.) So trying each port might be worth a try. I would also stick to thunderbolt to DP instead of using HDMI. What are your cable lengths?