I did a factory reset on my phone and it now updates . Just backup everything first and once it resets everything you backed up will Be back
I have this same issue.
"Update Now: Last checked on: 2015/05/13"
Also having the issue that MMS messages won't reliable send and won't reliably be received (unless I go into Ultra Power Saving Mode), which I believe turns off LTE.
I followed the advice of jcd0319 and did a factory reset of my device. It now updates. Caution, even though I did a "smart switch" backup, I still had to reset the layout of my pages on my device. Fortunately me email account and other settings were saved. It took me about an hour to complete, so do not attempt if you do not have a good wifi connection and have not performed a backup.
I was up for hours last night, and finally had success.
I was at 5.0.2 on my S6, and had the problem you described.
Smart Switch indicated I had that, too, but didn't have an "update" clickable where it shows it should in the help section.
I gave up, and poked around. I clicked to update the PRL and update the profile (buttons familiar to those of you on the system update part of settings). When I clicked to check for updates again--it for some reason worked.
Now, I would have totally not logged in to write this, but I further duplicated this with an unactivated Note 4 (using just for GearVR purposes). I did the same thing, updating the PRL and profile, and clicked to check for updates... and it worked. Never could have imagined it'd be that easy.
Of course, YMMV, and I'm very sorry if this does not work for you!
I tried multiple times to download the update after updating PRL then Profile but after updating Profile first then PRL it worked for some reason. Hope this helps.