I know this is an old problem and there was a lot of discussion in 2015. I rarely shoot tethererd at home but recently have had to (and will need to in the near future) and don't want to do any upgrades unless I really have to! I see all the problems were with El Capitan and I have not upgraded. I don't want Adobe CC so will upgrade to LR6 but only if it will acutally work. I have spent over $200 on tethertalk cables and TetherBoost Pro USB3 and I see that this is not the issue as I still can't get my D810 to be recognised for tethered shooting, the D300 is fine though!!
How can I get my Nikon D810 to shoot tethered into LR 5.7 on my Mac (currently still using Yosemite 10.10.5)?
Have you tried updating to the latest version of LR 5 which is Lr 5.7.1
Maybe another user of the Nikon D810 may offer some help.