I got my note 5 last week and have a Zagg glass screen protector which installed great. I have purchased 4 cases. I got the Best Buy Insignia clear soft shell when I got the phone. It looks terrible (the camera cut out is crooked) and only fit OK as its kind of squishy at the sides. Its going back. Then I ordered 3 Spigen cases from Amazon. The Thin Fit, the Neo Hybrid Carbon in metal slate, and the Rugged Capsule.
The Neo Hybrid looked the best with the carbon fiber look and the metal slate matched the color of the black sapphire pretty well. But, it added quite a bit of bulk (82mm width from the phone's 77mm) and it did not fit snug on the sides. When I would hold the phone in my hand the case would start pulling up the glass screen protector. Its going back.
The Rugged Capsule was a flexible TPU that fit pretty well, much better than the Insignia case. It did not remove the screen protector when using, but I just didn't think it would give me much drop or even bang protection. Its going back.
The Thin Fit is the one I ended up choosing. It snaps in place and does not move once it is on the phone. I have had similar thin fit type cases (Incipio and Poetic) on previous phones and really liked them. The Poetic protected my G2 from its only major fall onto asphalt while getting out of car allowing just a few scratches on the corner but no broken glass. The Spigen Thin Fit has cut outs to allow the use of the Note 5's actual buttons and the camera cut out has just enough of a lip so that it doesn't allow the camera lens to touch the surface when you set the phone down. The case does not add much bulk or weight and has good grip, unlike the Neo Hybrid which was slippery plastic on the sides, so I feel confident when I grab the phone.
Thank you to everyone on this forum for your info on the cases and screen protectors as it helped me make my decisions much easier. I wanted to share my experience as well.