Design of a Five Second Kill Switch
Yes, this is very easily done with a small microcontroller.  Even the cheap and tiny PIC 10F200 can do this.

However, your spec needs to be fixed up a bit.  First, what is "engaged" supposed to mean for a switch.  Proper terms would be closed or open, or even on or off.

Second, the 4 bullet points seem to make sense, but then you mention something about power going away and coming back being relevant.  So point 1 only applies immediately after power first comes up?  What if the switch is the other way when power comes up?