Assuming one eye is 5 cm further down compared to the other, would that somehow change perception if the brain has long enough to deal with that incoming information? For example, if you were born that way, would you be able to do depth perception and binocular vision just as well?
Would you be able to do depth perception and binocular vision just as well? This is hypothetical question. Hypothetically, the answer is yes.
The human brain has an amazing ability to adjust to changes to an individual's physical body. As evidence of this, consider the PD (pupillary distance) when you were born to what it is now. You have the same brain (in all likelihood), but that distance has undoubtedly increased significantly. Your vision continues to work exactly as designed.
This amazing flexibility is not limited to homo sapiens. Some species of actinopterygii are born with eyes on both sides of their head, but develop into fish with both eyes on the same side of their head. Their ability to hunt does not diminish after this change takes place.