How to fix a retaining wall that is difficult to access behind the house?
My neighbor and I fixed his retaining wall along the steps to his basement years ago (when we were both in better shape and in our late 20s).  We had it dug out by hand in a few hours, but it was mostly clay, and didn't require shoring up.  If you've got a long length, or sandy soil that's going to keep filling in as you dig, it might not be a good option, but it's really not that much work.

Digging out a pit isn't as hard as something like trenching, where you're always bending over ... with digging out the retaining wall, you can get in the hole, so you're not constantly bending over.

There are also plenty of ditch-digging equipment that could easily get through a five-foot opening.  If you really wanted equipment, measure how much space you have, and call your local tool rental shop; there's a whole class of 'mini-excavator' that might be able to get back there.  If you needed to loosen the soil, you could use a tiller, but then excavate by hand.