Sigarms,
I agree on all your points, and each installation/situation is different, and also agree geothermal is a great for new builds with land or water source for thermal exchange.
We have FHW Oil for primary heat and HW, and installed two ductless units in the house, one upstairs bedroom, loft area 900 SF, mostly for summer cooling, and a 12K downstairs in a 32x32 area for summer cooling and supplemental heat in the winter. We have 32x52 downstairs area which is "conditioned" in the summer - meaning the mini split cools the main area to 72-75* and keeps the rest of the house cool/comfortable.
in the 1000 SF detached heated garage / open concept office the 9K Hyper heat unit replaced an older Monitor kerosene unit for heat and ac as needed - this unit is probably undersized but maintains the space well unless the temp outside is below zero or above 90.
All are the Mitsubishi hyper heat models with no heating element in the pan.
Bottom line, for the OP, with 5 bedrooms to heat/cool, a distributed mini split system is a good solution once an HVAC assessment is done on current state.