There is VERY little information out there about
this, and believe me I have looked!
At this point your core is very weak -- you don't need to do things like sit ups to engage it and strengthen it, and any kind of "lever" motion like that is bad this early. The only ab specific exercise that I would consider safe after 5 weeks would be a gentle plank (start on your hands, like a push up position, instead of your elbows -- it's easier).
I think you'll be surprised to learn that easy jogging, especially when you transition from the elliptical to the treadmill, is a pretty good core workout. For that reason I would start with a week or two on the elliptical before you move to treadmill/outdoors. Personally I started running outside ~8 weeks post op and that was right for me.
I did not do any weight training while I had an ileo. The longest time between surgeries for me was 15 weeks and I did not feel comfortable doing weight training with an ileo that new. I'm sure many people will say that after six or eight weeks you're fine, do what you want. For me it was far more important to avoid a hernia than to do light weight training. I did go back to normal daily routine type stuff (so I probably lifted 20 lb worth of laundry, for example), but I stayed out of the weight room until ~3 months post takedown.
dx'ed UC pancolitis 5/12
past meds: asacol hd, VSL#3, apriso, rowasa, xifaxan, 6mp, cortifoam, pentasa, cimzia, canasa, butyrate, flagyl, cipro, prednisone, remicade, methotrexate, cholestyramine, cortenema
current meds: none!
step one: colectomy, end ileo 1/16/13
step two: j-pouch construction, loop ileo 5/1/13
step three: takedown 7/31/13