My J5 refuses to update to 6.0.1 It says: "The latest updates have already been installed."

I have 5.1.1 and I'm pretty sure I can update to 6.0.1...

Fix?
TL;DR: With F/DS model you are out of luck. Better stay with 5.1

In case of Samsung devices, there is a system called Customer Sales Code (CSC). It allows Samsung to provide updates sooner or later, depending on this code. For example, if I bought my phone in Poland, my CSC = XEO. It ends with "O", meaning Open. However, it's not that simple when you got your phone from carrier, because most of them have individual CSC to provide their bloatware. For example, if I get a phone from Orange Poland, I would get CSC = IDE. In that case, it would be my carrier that decides when I get an update, so even if entire world would already have 6.0, I may have to use 5.1 because someone at carrier HQ would be too lazy to confirm an update.

However, it's not a lost cause. With this app you can check your CSC (and many telemetry data used by Samsung, like how often you charge you phone, how many times you used headphones, etc. (they are almost worse than Microsoft)). Then check this list to see if it's Open version (it will have an asterisk). If your CSC is not Open and you see another CSC for your country that is Open, remember that CSC. If your country doesn't have Open, check neighbouring countries' CSC. If they also aren't open, google if any carrier in your country provides 6.0 update and google its CSC. Or even use CSC from Germany or Poland, it's not recommended but many people do it.

Then, when selected CSC, you have to either:


find ROM with selected CSC - this way you won't lose your warranty, but with F/DS model you are out of luck. You can browse http://samsung-updates.com/ and http://www.sammobile.com/ and compare your firmware IDs with the ones on website, but I don't guarantee they work. Then use Odin to install it.
install Cyanogenmod - F/DS=nope
root your device with KingoRoot apk so it won't trigger KNOX, and then: a) use CSC Changer app (go there and search for "S4"), b) use Root Browser or ES File Manager and do like this tutorial says (scroll to ES File Manager and follow up to point 8). Then after reboot search again for updates. If somehow KNOX triggered and you've seen triangle during boot, use TriangleAway and try searching again.