First, this is a really involved question. :) So I decided to split my answer into two parts, where the second part is a separate Q/A, involving how to activate a random wire.
This part of the Answer, takes that random wire (1 of 5), and multiplexes it with 5 buttons, to direct 1 of the 5 buttons to a valid-output circuit, and the other 4/5 to an invalid-output circuit.
Due to the diagram's complexity, I'm only showing 3 buttons, not 5 - however, extending it to 5 buttons is very straightforward, and should be clear from the diagram.
Top-level circuit diagram
The 5-Wires box is from the other Question. Basically there are 5 wires (gosh), exactly one of which will be active at any time, with the active wire changing each time a button is pressed. The wires are connected to a 222 circuit, which takes two inputs - a wire, and a button. The 222 circuit has two outputs, connected to two different 5-input OR circuits.
If the wire to a given 222 circuit is active, and the button is also pressed, it will send a positive signal down the red wire, to the valid circuit. The signal will last as long as a button stays pressed, roughly half a second I think. If the wire is inactive and the button is pressed, the 222 circuit will send a positive signal down the green wire to the invalid circuit. In all other cases, there is no signal sent down any wire.
222 Circuit Diagram
I have tested the individual components in isolation. The 222 circuit works fine, the 5-clock and 333-circuit in the other part, work fine - but I haven't wired up an entire test circuit (not even 3 buttons), because it's really freaking big. However, as far as I can tell, it should work - there are no parts that require extremely precise timing, I turned all the corners on Redstone wiring as needed to avoid glitches, and I don't see any section that would be affected by the SW rule.
I also don't have Baezon's MCE, since it uses Java 6 (I have JRE 5). It might be easier to enter and test in a simulator than doing it by hand, which I was. :) If it doesn't work, let me know what part broke.
The entire circuit is fairly complex, with a lot of wires crossing, but I don't see how you can avoid that. When you're connecting 5 wires to 5 buttons, and directing each result to two other circuits - that's a lot of cross-overs.
The 222 circuit is fairly mundane, I claim no originality - the only reason I gave it a name, is I had to give it some label in the diagram for clarity. :)