I would advise you use 8.2(5) as it is the latest release in the 8.2 train. It will work fine without changing the configuration file command syntax from your 8.0(4) system.
Only when you go to 8.3 or later does syntax change significantly. You would also need to confirm the required additional memory (1 GB for the 5520) is present to run 8.3 or later. (9.1(4) is the latest overall version as of this writing.)
No matter which ASA software you decide on, you should go ahead and move your ASDM up to the recomended 7.1(5).
Note that the 5520 went end of sales this past fall and that there will be little or no further development of the 8.2 software line as none of the new X series ASAs will even run that older code. That said, 8.2(5) is quite stable and mature.
