The 05 Chopper can be loaded with issues. It was not there best year of QA. The TP boxes have the wrong geometry so the rockers are sliding on the valves and wear them out. My valve guides were shot at 3k. My pistons were gunked up with oil. You can see the mark on top of the valve stem. Also clutch was improperly installed at the factory, missing spacer and nut not installed correctly. Apparently common in 05. Not trying to dissuade you, just don't overpay because there will be work to do. You will likely need a new EHC for $500 in the near term.
The stock 05 motor is also fairly anemic. Many had EPA restricted valves, undersized carb and a restrictor plate behind the intake manifold and could use a cam upgrade. You are limited to the 585 cam unless you upgrade the valves and springs.
If you remove the restrictor plates you will need to find spacers to replace them behind the intake manifold. If you upgrade the carb you will need a new manifold and can eliminate the spacers.
If I had it to do over I would get a 2006 which came with S&S rockers or a K9 which benefits from a larger gas tank. 4.4 vs 3.8.
https://imgur.com/a/Gp4F7Dr