Hi Everyone!
I just got straight talk active on my iPhone 5S! It works the same as my iPhone 4S!
Here's the combo I used:
Apple iPhone 5s 16GB (Space Gray) - Unlocked
and
Straight Talk iPhone 5 Nano SIM Card for AT&T
Check out the links below to help work through common issues:
Activate Straight Talk Wireless on an iPhone 5S
Fix iMessage bug on iPhone 5S
Oh... Youll need to modify the SIM card a smudge if you buy the normal size SIM
Good Luck!