The 5/31/2016 date came from http://www.verizonwireless.com/support/software-updates/, the link itself either isn't updated yet or the update is going to be a security patch.
I'm most definitely NOT a VZW employee. If a post answered your question, please mark it as the answer.
I updated my GS5 to 6.0.1. The download and installation took well over a half hour due to the file sizes. I briefly panicked after the phone came back up because it looked like none of the applications I had previously moved to my SD card to save space carried over -- icons were grayed out and clicking on them gave a message that the app was not installed. However, the phone soon rebooted again and the apps all appear to be working now. I haven't had time to play with it and am back at work now, so my fingers are crossed.
I did activate the HD calling feature so that I could activate Wi-Fi calling, then deactivated the Wi-Fi calling for now. I'm just thinking this will come in handy next time I travel to Canada, but not much use here where VZW has strong coverage anyway.