Wow, that's a big pot o worms you opened with that one brother, lol.
I voted yes about the 5th dimension, but the reality is that, what you are talking about is the spiritual dimension (realm). I think that when we cross over into the spiritual realm, that things can be healed, but may or may not depending upon what it is that is Gods will about that person. I don't think it's automatic about physical healing until we are transfigured in the twinkling of an eye when the Lord returns.
When Jesus was crucified, there was an earthquake and the veil was rent in two, that this was Gods way of telling us that all of the people have full access to the kingdom realm now. No more do we have to go to the priest or wotnot.
my understanding is that very few people find this though. Through their preconceptions & beliefs, they have their own internal veil. Having eyes but can not see, ears but can not hear etc.. Myself even, I have never visited the kingdom realm or seen a parting of the veil so that I could see into it.
My belief is that we have full access, and should be living with that knowledge. There's clues all throughout scripture about this:
Matthew 6:10
10 Thy kingdom come, Thy will be done in earth, as it is in heaven./
Matthew 5:8
Blessed are the pure in heart, for they will see God./
Acts 2:17
17 And it shall come to pass in the last days, saith God, I will pour out of my Spirit upon all flesh: and your sons and your daughters shall prophesy, and your young men shall see visions, and your old men shall dream dreams:/
There's more. Crossing into the kingdom realm can be done in spirit, or physically, that's up to the Holy Spirit. 2 Corinthians 12:2, Revelation 1:10
The kingdom of heaven is at hand, meaning right here, right now. (Matthew 4:17) meaning, not, "out there", but here, in us and available to us. Seek God and find Him. (Matthew 7:7)