To try and understand the Ramabam's question I think we have to first provide an explanation that will remove ones initial understanding of the the Rambam's question. I don't believe God's knowing what we will do in the future contradicts free will. The first step is to define free-will. I would like to offer a suggestion that free-will is when one is the cause of their own good or evil. The main emphasis is that mankind is the cause. Now, let me offer the following example to resolve the issue. Let us say that Person A, Mark, is watching a fire start at the bottom of a house. If you ask "Mark", do you know that the house will burn down? He would respond of course. Now, just because "Mark" has knowledge that the House will burn down, does that make him the cause of the house burning down? Of course not. Knowledge does not equal causation. Similarly, as we established before, Free-will is where Man is the cause of his own good or evil. Just because God knows what man will do, does not make him the cause. Man is the cause. So, really the question just drops away. So then what is the question the Rambam is really bothered by?
Perhaps the question the Rambam is asking (in Teshuvah 5:5) is how to reconcile Hashems knowledge with the premise that Hashem knows what man will do. What the Rambam is trying to clarify is how Hashem knows what man will do. If the way Hashem knows is the same way a watchmaker knows how a clock works, which is that he knows all the causes that went into making the watch, therefore he can predict the results by tracing the chain of causality. Similarly one might suggest that the way Hashem knows what we will do is because he created the world and knows all the causes that went into the creation. So, if he knows all the causes he can trace the chain of causation from the beginning of time and know exactly what will happen in the future. However, if this is the way Hashem knows, then this would preclude Free Choice. Because, Free choice is where man is the cause of his own actions, their is no other cause. Meaning that man is operating outside the chain of causality and is the prime mover of the decision. Therefore if the way Hashem knew what man will do, is via this chain of causality, Hashem would not be able to know what man will do if Man has free choice. So the Rambam is setting up a contradiction between the way Hashem knows things and the premise that man has free will. I believe the Rambam answers the problem by saying that the way Hashem knows things is not through knowing the chain of causality (as a human creator of something might know) but rather the way Hashem knows things is through a different way that does not contradict free will. This third way of knowing is something we can not fully grasp. Hence, the contradiction is removed.
I hope this is clear, please do not hesitate to ask for further clarification.