The Poisson process that you're using assumes that 0.05 is the expected number of computers failing in one day in an unknown number of total computers (your answer also assumes that computers failing multiple times is allowed or else there is such a large number of computers that this is negligible).

The independent probability that the student is using assumes that there are exactly four computers each of which has a 5% chance of failing.

The wording makes it sound to me like 5% is the chance of any individual computer failing (so the second interpretation).  In that case, we want to know the total number of computers and apply a binomial distribution.  Since the question doesn't give the total number of computers, it can't be answered.