Last time for everybody. Rand (and all materialists) have no logical, coherent, non-contradictory explanation for the trustworthiness of our senses.
Yes she does, and you'll find it in her epistemology.
Starting with a baby's view of sense perceptions (total chaos) Rand develops an epistemology based in reality and reason that acknowledges human fallibility in interpreting sense perception -- while at the same time demonstrating human capabilities for immense achievement (Rand's own achievements are a good example) when one remains focused on sensual inputs from reality, and finds sense within reality using reason.
And for the last time your statement is fallacious because you can't prove a negative! Your very statement is dependent upon the stolen concepts you reject; that there are any such things as logic, coherent, contradictory, explanations, trustworthiness or senses which make absolutely no sense without the premise that these things exist which can ONLY by verified by the senses.
Your unprovable negative assertion is self refuting.