Yes, a 5 counts as a success on the Computer Dice.
A Computer Dice (Die! Die!) is always rolled when you're doing things. The Computer Dice may also be the only dice rolled. So when the rules say, Each rolled dice that shows a 5 or 6 is a ‘success’ it is referring to all the dice the player rolls, which includes the Computer Dice and may indeed be only the Computer Dice. However the phrase Each of the dice rolled will never refer to a pool of dice not including the Computer Dice.
This rule would also refer to any additional dice which are gained through other means, because again, it says Each rolled dice. Which means each dice the player rolls.
There is also an example later on of what happens when you have a negative NODE (p. 26, emphasis mine):
If your NODE dice number for a particular task is negative, treat the negative number as a positive and roll that many dice – plus the Computer dice, of course. However, any dice that don’t show 5 or 6 subtract from your score rather than simply not adding to it – so if you rolled 4 dice and only 1 showed a 5 or 6, then your overall score is 1 minus 3, making -2, which is a pretty bad score.
Here the rules state if you rolled 4 dice and only 1 showed a 5 or 6. The Computer Dice was already mentioned as part of the calculation, so it's quite clear that the Computer Dice is included in the dice pool, and the rolling of 5 or 6 includes the Computer Dice.
There is never any indication that a Computer Dice is treated differently than the other dice, except when a computer is rolled.