Hi Tom, would the living floor of the house be sunk into the hill and the basement of the house be deeper underground? Or is the basement a "walk out"?
It sounds to me like having a basement with 4-5' of earth above it to keep the cold down is excessive. Just surrounding the basement with cold soil on the bottom and sides plus the natural stratification of cold air seems to me like it would keep the basement cold. I believe 1' of insulation in the floor would have more of an R value than 5' of dirt.
Check out the My Little Homestead videos on their MusArt underground studio for some ideas: