Logicizing randomness I haven’t had time to read all the responses so excuse me if I’m repeating a previous comment.
If we consider the all too human component of this thought experiment, us, we must not fail to consider the fact that our brains are pattern detectors. This somewhat negates the classical notion of randomness in my mind. Ultimately it is nothing more than a lack of information on our part, what we consider randomness essentially is somewhat synonymous with inexplicable. Even when considering this through the lens of probabilistic outcomes, that something with a vanishingly small likelihood of occurring happens, seems more aptly attributed to desirability bias - this shouldn’t have happened! It had a one in all but infinite probability of being the case! - which I think also treats the issue of the original post and addresses what responses I did get through.
That said, another plausible interpretation of randomness (though only subtly different, it is philosophically distinct) is unpredictability. In this sense, the case of 10 5’s appearing and being an unsatisfactory result from the randomness machine would entail you A) had an expectation of what the randomness should look like or B) any result with too much of a “common” pattern would be unsatisfactory and make the machine seem faulty.