Of course I wish you luck, but the plan seems to be the following:

2 hours: Transit ICN-Seoul and vv

1/2 hour: subway travel

1 1/2 hours: subway station to museum, see museum, and walk back to subway

X hour: do something else

This totals to 4 + X hours already out of 5.5 hours total scheduled time on the ground. You need to get through airport upon arrival, go through immigration and customs, find transportation, get ticket, and possibly wait. At the other end, assuming that you already ahve your boarding pass, you need to clear passport control and security, walk to gate, and be on board a half hour before departure.

To me this just doesn't compute. Also, there's absolutely no extra time for disruptions, getting lost/disoriented, long lines, etc.