Help! My friend punched a metal door 5 days ago & his hand is still swollen & in pain. Should he go to the er?

Hand injury. He may well have a fracture or some complication due to the injury. He should see his doctor or go to the er to find out what has happened to his hand. It is important as if complications occur he may lose function of his hand if infected he may be in serious trouble.
Yes. Likely a "boxers" fracture...... So yes, needs an xray.