I am enjoying this dialog, in part, because I sense that you and I have similar aspirations. For example, I am trying, in my own idiosyncratic way, to legitimize the concepts of Metaphysics and Spiritualism, which were banished from scientific and philosophical discourse most decisively by Descartes. His Body/Soul division was later called "non-overlapping magisteria" by S.J. Gould. It gave science license to investigate all of Nature, except the aspects we are all most intimately familiar with : our own experiences & feelings & ideas. Yet those of other people remain shrouded in myths and "spiritual mysteries".
The so-called "Enlightenment" was a necessary correction to the Dark Ages. IMHO, It was justified in rebelling against the dogmatic magisteria of the combined church & state of the Holy Roman Empire. Since then, Empirical Science has gained dominance among the intellectual elite, while Spiritualism, in its many incompatible forms, still dominates the lives of the non-intellectual masses. Apparently, like me, you feel that this attempted amputation of Soul from Body favors one part over the whole system. But most attempts to patch the rift tend to favor one side over the other : Reason vs Emotion. Even the empiricist philosopher, David Hume, noted that "Reason is, and ought only to be the slave of the passions." But he was not advocating a return to the submission of individual reasoning to collective passions in the form of organized Religion. Instead, " All I insist is that it is fantasy to pretend that reason can provide the fundamental foundations for our hopes, ambitions or morality". My proposed patch for the Matter vs Mind split is the BothAnd philosophy.
Bernardo Kastrup, in the book I'm currently reading, is also on the same mission. But we are all approaching the goal from different directions. He even seems to have a concept similar to your Fifth Dimension. He observes, "since we all seem to share the same world, there has to be a broader cognitive space --- beyond just perceptions". He describes that "higher dimension" in spatial terms resembling yours in the quote above : "a cognitive space not only comprising, but also surrounding, perception". His "space" is also transcendent in a sense that you might agree with : "consensus experiences live in a transpersonal cognitive space, instead of an individual mind." You'll have to read the book to see how he defines his personal "consensus reality". Hint : it's not simply objective reality, or socially-constructed realty. Anyway, the point of the book seems to be that we know and discuss that transcendent reality in terms of symbols, myths, metaphors, and analogies. Kastrup seeks to reconcile the thousands of contradictory mythical narratives by discovering their essential commonalities, as suggested by Joseph Campbell, in Myths To Live By. I may not completely agree with his prescription for what ails the modern fragmented world. But we seem to be looking in the same direction.
Consensus Reality : https://en.wikipedia.org/wiki/Consensus_reality
BothAnd Philosophy : http://bothandblog5.enformationism.info/page6.html