You will want 2 counters, 1 counter will track how many have been pressed and the other counts how many were correct.
Each time a button is pressed:
Check the button counter is equal to the order you want it pressed in (IE on the first button you want to be correct use a check to see if the button counter is = 0, if true add 1 to the correct counter)
Use a disable element on the area check so the button cant be repressed again instantly.
Add 1 to the button counter with a delay of 100.
Check if button counter is = 5 with a delay of 200
If true then all buttons have been pressed, so on the true output you do a check to see if the correct counter = 5.
If its true you can activate whatever you want.
If its false you set both counters back to 0
change the buttons doodads to pop back up, you can link a single change doodadstate to all of em. Add a delay of 1000
use enable element on all of the area checks so they buttons can be pressed again, with a delay of 1100.
I'm not brilliant at explaining it in words but if you can follow it you should have a functioning puzzle.
If you want it random every play through it becomes a bit more complexed but its possible, just a lot harder to explain in chat.
