The are many things that can cause the '05 to go to limp mode.
Engine:
Overboost: If I remember correctly it will limit rail pressure to 20kpsi, and something else.
If an injector harness shorts to ground, the computer will drop those 3 cylinders (the front 3 or the rear 3, whichever half of the engine had the problem).
There are many more.
Transmission:
Over temperature, 265* or something, the torque converter will lock and default to 2nd gear.
Loss of overdrive relay will get you stuck in 3rd, but you can swap out the heater mirror relay to prove the relay itself is at fault.
Loss of speed sensor will default you to 2nd, since the truck doesn't know how fast it is going.
A lot of the time, a key cycle will get you rolling again if you are in the middle of nowhere. But checking code(s) are ideal.
2005 2500 Cummins/48RE/3.73, QCLB, 4wd, BigHorn, Edge Juice w/ CTS + Turbo Timer,Transgo Shift Kit ISSPro Oil and LP pressure gauges, GDP 20/2 filters, Custom Diesel Steering Box Brace
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Honda EU3000I Genny