Depends on the tools
25 cubic feet of soil is about 2.5m3 and weighs between 3 and 4 metric tonnes. A shovel full of soil is about 10kg of material so we’re looking at 300-400 shovel fulls.
From a loose stockpile, I can move that with a shovel in about 3-4 hours and I’m a middle-aged office worker. A fit, young adventurer could do it in say 1-2 hours.
Of course, this isn’t a loose stockpile – this is digging a hole and that’s much harder; particularly the deeper you go. So double that. If it was hard-packed and needed to be mattocked first it would take about double it again. This is, of course, working at a sensible pace – working flat out in a life and death situation – you could shave 10-15% off, maybe more if you worked in shifts.
5 feet deep is approaching the point where the excavation is at risk of not being stable – most excavation codes require protection once you start to hit those depths. In clayey soils it might hold up a little better – in sand, you are going to need to batter that sucker so you need to remove about twice as much material.
Of course, with a 30-tonne excavator, I could move it in about 3 minutes. If I didn’t have a shovel, we’re talking days.