What should I do about this bowing foundation wall?
You have 1 advantage that the wall is only ~5’ below grade. Can it be repaired DIY yes, but this would be quite involved.

I would suggest digging out outside the wall for 2 reasons:

it would allow backfilling with gravel so it could drain and the hydraulic forces would not push it in again.

The second reason a temp wall set inside to support the home will allow rebuilding.

I would suggest removal of the brick a new footing being poured and a cinder block wall reinforced with rebar being installed once the wall is built, back fill the blocks with concrete. Then seal the outside of the blocks and backfill with gravel.

When I want good drainage I use river rock, not crushed quarry, because crushed packs tighter and doesn’t drain as well. 

I would warn this is about as bad as I have ever seen and it really needs to be done prior to collapse. I would be looking for other issues like roof leaks, doors not closing or cut to fit so the door is not square , window problems etc.

You may have all of the above, if I liked the house I would tackle it but I grew up in houses under construction repair and continue today.