Which iOS IPSW file is the right one for my iPhone 5S?
As you can see from the ipsw.me website Apple have released two slightly different versions of iOS 9.3.2 for the iPhone 5S. By looking at Apple's developer website I can see that one version is for iPhone models A1453, and A1533 and that the other is for models A1457, A1518, A1528, and A1530. 

Unfortunately the ipsw.me website does not directly identify which IPSW is which, but by selecting each of them in turn we can see their file names. These file names contain the hardware string for the kind of iPhone they should be installed on.


iPhone 5S (GSM): iPhone6,1_9.3.2_13F69_Restore.ipsw
iPhone 5S (global): iPhone6,2_9.3.2_13F69_Restore.ipsw


According to this website:


Models A1453, A1533 = iPhone6,1
Models A1457, A1518, A1528, A1530 = iPhone6,2


You'll find your iPhone's model number on the back of the case (it will start with "A1"). 


A1453, A1533 and you need the (GSM) IPSW from www.ipsw.me
A1457, A1518, A1528, A1530 and you need the (global) IPSW from www.ipsw.me