The validity of the senses is not subject to proof, because it is a prerequisite to the very concept of "proof' - to prove an idea is to reduce it to perceptual observation. It is an axiomatic truth, as one must implicitly assume the validity of the senses in any attempt attempt to deny it. To claim that the senses are invalid is to use knowledge ultimately based on one's own sensory experience to reject the very basis of that knowledge.
Although the validity of our senses is axiomatic, it still can, and should be explained. The traditional intrinsicist/religious attempt at validating the senses consists of positing some sort of supernatural cause to it. Aristotle's idea that we can perceive reality because we have some sort of divine metaphysical essence, exemplifies the most rational forms this approach can take. Leibniz, on the other hand, shows how irrational this premise can get with his idea that the senses do not have to be valid, but the Christian god makes them so simply because he is good.
There are two fundamental problems with the intrinsicist approach. The first one is that it bases sense validity on faith and supernatural ideas, pitting the very starting point of rational thought against the secular conclusions that come from it. The second is that it essentially dismisses the very issue of validating the senses - to say that the senses are valid "because God said so" is not to discuss the validity of the senses, but to put an end to any rational discussion about it.
As our culture developed, our intellectual discussion turned to the undeniable difference between our perception of an object, and the object being perceived. Facing that difference, subjectivists like David Hume and Immanuel Kant had the same answer, which roughly amounts to "since perception and existence are always different, it is impossible to use perception to know reality, however similar they might be". This split philosophers between modern theologians, who attempt to breathe new life into traditional mysticism; those who took that premise to its logical conclusion, and rejected reality altogether; and those who attempted to justify some sort of knowledge on those premises, and inevitably failed.
Part of Ayn Rand's genius was acknowledging the difference between perception and existence, while fully rejecting the subjectivist answer. Her reasoning can best be summed up as "Since perception and existence are always somewhat similar, however different they might be, perception provides a direct link to reality - the only one we have". To perceive is to perceive by specific means - to retain and automatically integrate automatic interactions between our sense organs and existents.
The difference between direct perception and reality is the very reason we need concepts. The direct perception of a dog will only provide me with itself, and no other information. Integrating direct perception into conceptual knowledge requires establishing the relationship between the percept and its two causes: the entity and the means of awareness. I will talk about this process in a little more depth tomorrow.