I'd say that for myself, I'm not declaring for sure there is nothing beyond our five senses, there's certain wavelengths we cannot see that we've found through science, and there are things in quontom physics like one particle being in two places at once, or different places depending where you look for it, that at first blush make no sense whatsoever.
However I believe strongly in objective truth, and a persons claim that a supernatural event has taken place is not sufficient for me to believe that thing actually happened. To be pithy, I don't think physics stopped working so you could experience your dead great grandmother haunting you. Either there are ghosts, or there are not ghosts, your feelings don't bear on the issue.
I am not saying we have solved all of the mysteries of the universe, I'm saying that we're on the path to eventually doing so.