List all of processes running in the last x minutes
 

How do i record (or find log) of all commands/tasks/processes that linux executing/executed in the last, let's say 5 minutes?

So basically, I need something like ps auxww result, but record in real time for the last x minute.

Thanks.

You could use sar. It is in the sysstat package. Set it up to run the sar data collector. That will put the information into a file that you can read with the sar utility.