Have previously been able to signin and sync to iPad and iPhone all my smartcollections.
With this latest update to Lightroom (5.7.1, raw 8.7.1) and CC on Win 10 PC, wherever I go (Lightoom or CC) to try to signon to mobile, gets in endless loop and never asks for login info. I've left it sit one tie for 15 minutes.
What Bit version of Win 10 are you using?
LR is now up to 6.9, stand alone perpetual license version, or CC 2015.9 for the Subscription base version (Same program, two different licensing options).
Since you are still using LR 5 (5.7.1 which came out well over a year ago. Months before LR CC 2015/6 was released in 2015) I suspect your Bit version of Windows is 32. Even if you are a subscriber to the Photography Subscription plan the newest version of LR can only to be installed on a 64 BIT operating system.