Algorithm Question.

You're telling the lift what to do when someone presses a button... so, if someone pushes a button on a floor, you tell the lift to go up to that floor. How does it know how to go to that floor? Well, you'd take the current floor, and the floor it needs to go to, multiply them by 5 and find the difference in distance between the two, then go up or down that many. You also need to work out what to do when someone pushes a button inside the lift: that's essentially the same thing.

With the open/close door sequence, you have a bit of choice... the easiest one for you to do in an algorithm is probably to have the doors close a few seconds after a button is pressed inside the lift, and open when the destination is reached (and remain open on that floor, but not any others). Then you could add a step that checks if there are any passengers inside the doorway, and if there are, open the doors and close them again a few seconds later.

Then I suppose there's the emergency stop button, which sort of speaks for itself

You basically need to write what I've said for each 'sequence' (lift call, button inside lift, open/close doors, emergency stop) in a sequence of steps.