* Engine Mounts: The engine mounts are different. You'll need custom mounts or significant modification to the existing ones.
* Wiring Harness: The 2005 6.1L Hemi's wiring harness is completely different from the 2001's. You'll need to either adapt the harness extensively (extremely difficult) or use a standalone engine management system (expensive and complex).
* Transmission: The transmission compatibility depends on the transmission in your 2001 Ram. You may need to replace it with a transmission compatible with the 6.1L Hemi. Even then, the bellhousing may not match.
* Computer/ECU: The 2001 computer will not work with the 2005 engine. You'll need the 2005 computer or a standalone system.
* Exhaust System: The exhaust system will need modification or replacement.
* Driveshaft: The driveshaft length might need adjustment.
* Cooling System: The cooling system might need modification.
In short: It's a project that requires significant fabrication, electrical skills, and extensive knowledge of automotive systems. Unless you have significant experience with engine swaps and are comfortable with extensive modification and potential unforeseen problems, it's best to consider this project infeasible for a novice mechanic. The cost of parts and labor would likely far exceed the value increase of the truck.
A more realistic approach might be to rebuild or replace the existing engine in the 2001 Ram, or find a used 2001-2003 Hemi engine for a more straightforward swap.
