I believe small children COULD have extra-sensory perception. Obviously, I am not in a position to know. I agree with the comment from "It's Just Me" that we could be born with senses that we are taught not to use or that get shuffled to the back, to use his (or her?) terms. It would make sense as an early learning tool to have means beyond those we normally consider to learn and adjust to the world. When we have done this, perhaps those senses are "not needed" anymore and become dormant from lack of use.
It would also help explain extraordinary stories such as Hellen Keller, who learned to communicate with virtually no exposure to traditional communication methods.
Shelly@G.P.R.G. makes a similar type of comment. We are told what to believe and what is real, and also what not to believe in. Another way to put it is we are told what is real or given a "description" of the world that becomes our reality. Whatever does not fall into this description is lost.
After all, who says we have "only" five senses? Perhaps we have 20 and only use five. Who knows?