First, there is no guarantee that after you jack it and put the load back on the original foundation, that it won't just start settling again with it's new load. I suppose the only way to find out is to try it. If it keeps settling after then you might want to create some new, deeper footings inside your original foundation walls and re-support that corner of the house with new posts and a girder beam of some sort, maybe.
5" is very significant settling. Aren't there cracks in the foundation wall itself? It is hard to imagine the one corner dropping 5" and not cracking the foundation walls themselves.
You really need to jack it just a little bit at a time, over a period of days and probably over a couple weeks. It is going to want to stay the way it is (bent floor joists) because it has "set" that way.
I would want to be sure that there is no rot in the sill and/or box joist and joists and bottom of wall studs. This is part of determining exactly what has happened. Can you put a long straight edge, or stretch a string in the basement to determine exactly how much the foundation has sunk? If the foundation sunk 3" and the floor upstairs is down by 5" then you might have 2" sunket b/c something has rotted and compressed. You also need to survey the "top of the wall" height at your eves/roofline to confirm that the wall and/or ridge, etc. has actually settled. If not, then your trouble may be in the floor more than in the foundation. You need to be sure that you have an accurate survey of exactly what is happening before you proceed.
How you jack it really depends on how it was built. If you can only jack from inside the basement, pushing up the joists, then you have to confirm that you are transferring the lift load to the outside walls, if necessary. Sometimes, by putting a strong girder beam across the bottom of the joists then the load will automatically carry under, and lift the walls. Sometimes not, depending on how it is framed. Some floors ride inside the studs above (older construction technique) and some floor have the studs sitting on top of them (newer). Some older framed houses, you are better off lagging blocks to the studs outside the house, putting a beam under them and jacking the studs to lift the floor and sill. What I'm getting at is that specific, detailed instructions cannot be given with 100% certainty by anyone that is not there looking at it (assuming that person is qualified). You need someone to come look at it.
There is also the issue of the footing for your jack. If you are jacking in the basement, you don't know if you are going to end up breaking up a poorly supported segment of the slab. There are also many safety issues to consider. If something fails after you have jacked it up 5" who knows what will happen if it drops that 5" because the jack goes through the slab or something else lets go? Bad things can happen. If jacking on the slab then you need to spread out the load with cribbing and/or beams, etc.
I'm sure others will chime in with other ideas and details, etc.