Ford "thrifted" PATS for the 2005 model year, then it returned on V6 models for 2006 and then on all Rangers from 2007 on. They must have received some complaints.
Your truck has a key that looks like a PATS key and there is a Theft light in the cluster but your 2005 does not have PATS.
2003 FX4 Level II, Supercharged 5.0L V8, Headers, Duals
BW4406 manual transfer case, Aussie Locker, Torsen L/S, 4.10's
Bilstein 7100 rezzies, Cadillac/Mustang rear discs, Duff traction bars
Keypad Entry, Lock LEDs, ABS switch, sway bar discos
Heated seats, Explorer EATC, Trip Computer and consoles
2003 XLT 2.3L M5OD-R1 reg cab beater, 2011 Taurus SEL, 2016 C-MAX Energi Plug-in Hybrid