I agree with Gaz that 5 days each is overkill (at least at this point).
Also agree with Cezaur that your fat loss should come from diet adjustments. Of course, training is important, too.
With your situation you need efficiency. Spending hours with weights and on the elliptical will likely be counterproductive, as it will stress many of your body's processes and inhibit fat loss and/or muscle development (generally, the two don't go hand in hand, though there are some minor exceptions..).
I think you could handle 3 days of each at low volume. You need to focus on intensity. This takes a lot more focus than just "jogging" or what have you but it's worth it in the end.
For cardio, you CAN run on your weight training days. There are benefits to that such as increasing blood flow to the now-damaged muscles, which can speed up the healing process. However, I've always preferred doing my cardio on days off from the gym. This is especially useful if you train your legs throughout the week (as I do). I squat and deadlift three times a week, so to run on those days isn't the most efficient use of my body. My cardio performance is several times better when I'm fresh on an off-day.
But I digress -- something like three times a week at 15-25 minutes TOPS. You can do HIIT (high intensity interval training), which is actually a healthier way to progress. Just remember to warm up and stretch afterwards.
For weight training, a very modest full-body 3-day split would be a good idea. Something like...
Tues: Push
1 - Back Squats
2 - Flat Bench DB Chest Press
3 - BB Military Press
4 - Planks x 2 - 4
Thurs: Pull
1 - Deadlifts
2 - Lat Pulldowns OR Pullups (if bodyweight is too difficult for reps)
3 - DB Unilateral Rows
Sat: REPEAT TUESDAY'S PUSH WORKOUT
FOLLOWING WEEK REPEAT WORKOUTS BUT ALTERNATED TO ALLOW EACH LIFT TO BE PERFORMED EVENLY
So, you could do 2 weeks to allow each lift to be performed equally, then switch rep ranges/intensities. Something like this..
Week 1 + 2 -- 3 x 10 @ 12RM
Week 3 + 4 -- 4 x 12 @ 14-16RM
Week 5 + 6 -- 3 x 8 @ 10RM
Week 7 + 8 -- 5 x 5 @ 6-7RM
Follow something like this for 8 weeks. As I always say, I'm not necessarily saying follow this exact routine. But, this is a good idea of what to do.