If your S5 has network (carrier) branded firmware (a '3' splash screen on boot up, 3 apps preinstalled, maybe some things disabled like Wi-fi calling) then it's 3's responsibility to release it's branded firmware into the cloud for your phone to latch onto and get an update (all Samsung servers, but 3 have to 'tinker' with the unbranded one and hand it back to samsung). If it is "unbranded" with no network apps etc. (To find out for sure you need your CSC code dial *#1234# into the dialler and Google the CSC code, any of the top five Google results will tell you) it is Samsungs.
My guess is that the S5 is no longer supported by either 3 or Samsung, and possibly both.