There are several potential answers to your question. The simplest is that the year 5773 is counted from the creation of Adam and not from the beginning of the creation.That means that there are five and a half days until Adam was created that cannot be quantified in any way.
Below is one approach given by Rabbi David Gottlieb. There are other approaches as well - I suggest the book Thinking About Creation by Andrew Goldfinger and also Fossils and Faith by Natan Aviezer.
The contradiction between the age of the earth and the universe according to science and the Jewish date of 5773 years since Creation has two standard solutions. The first allows that the scientific estimate could be true, and show how the text of Genesis can be reconciled. (See Challenge, eds. Carmell and Domb, (1978: Association of Orthodox Jewish Scientists), pp. 124-41, 164-75.) The second is that the Jewish date is the literal truth, and the scientific estimate must be explained (away!). (See ibid., pp.142-49.) Since you ask only about the second solution, I will only address it. But I recommend that you take a look at the first solution also.
The second solution says that the real age of the universe is 5773 years, but that it has misleading evidence of greater age. The bones, artifacts, partially decayed radium, potassium-argon, uranium, the red-shifted light from space, etc. - all of it points to a greater age which nevertheless is not true. God put these things in the universe and they lead many to the false conclusion of a much greater age.
Let's first understand that God certainly can do this if He wishes. There is no logical impossibility in imagining such indicators of false age. Furthermore, something like this is part of the naive understanding of Genesis. Adam was created as an adult. Observing him a few minutes after he was created, we would assume him to be at least twenty years old: he was created with misleading symptoms of greater age than he possessed. The trees created in the Garden of Eden presumably had tree rings. Tree rings usually indicate the age of the tree, but in this case the rings are misleading evidence of age the trees did not possess. So the idea is not inherently absurd.
The usual response to this idea is: "Why would God do that? Why would He want to mislead us in that way?" Now strictly speaking we don't have to answer that question. Knowing why God would do it is not a prerequisite to asserting that He did it. Often we don't know why people do various things; that does not lead us to doubt that they did them! Nevertheless, even though we don't need to answer the question, we can. Briefly, the purpose of the physical world is to hide God's presence so that we can exercise free will. In fact, the Hebrew word for "world" - olam - means "hiding". So evidence which hides the true age of the universe since Creation would be part of the general policy of hiding God's presence.
A more sophisticated objection to the second solution is this. Can we not defend any arbitrarily chosen age for the universe by this logic? If we said the universe is 50,000, or 500,000, or 5,000,000 years old, we could always say that the evidence of greater age was due to misleading evidence put there by God! Doesn't this trivialize the whole project? It means that there is no objective standard at all for deciding how old the universe is!
The answer to this objection is as follows. Indeed, if we were to use this logic without any limits, it would trivialize all investigation in the age of the universe. But we are suggesting that it be used to resolve a contradiction between two generally reliable sources of information. Under these conditions it is wholly appropriate. I will give you an
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