If your primary goal is weight loss, you need to make sure that cardio is a part of what you're doing. Based on what you said about your nutrition, do what you can to eat at or slightly below maintenance. Given that you have 5 weeks, you have time for a skinny HST cycle. I'd recommend that you keep things very simple - Bench Press, Chins, Squats, Overhead Press, Deadlifts in an A-B type workout. Start every workout with 15-20 minutes of moderate-intensity cardio. Do post-workout cardio as well - walking or very light jogging only.
So - I'd lay it out like this:
Monday, Week 1: Bench, Squats, OH Press, Chins 2 x 15
Wednesday, Week 1: Bench, Deads, OH Press, Chins 2 x 15
Friday, Week 1: Bench, Squats, OH Press, Chins 2 x 15
Monday, Week 2: Bench, Deads, OH Press, Chins 2 x 15
Wednesday, Week 2: Bench, Squats, OH Press, Chins 3 x 10
Friday, Week 2: Bench, Deads, OH Press, Chins 3 x 10
Monday, Week 3: Bench, Squats, OH Press, Chins 3 x 10
Wednesday, Week 3: Bench, Deads, OH Press, Chins 3 x 10
Friday, Week 3: Bench, Squats, OH Press, Chins 3 x 5
Monday, Week 4: Bench, Deads, OH Press, Chins 3 x 5
Wednesday, Week 4: Bench, Squats, OH Press, Chins 3 x 5
Friday, Week 4: Bench, Deads, OH Press, Chins 3 x 5
Monday, Week 5: Bench, Squats, OH Press, Chins 4 x 3
Wednesday, Week 5: Bench, Deads, OH Press, Chins 4 x 3
Friday, Week 5: rest, stretch.
Progress your loads on a weekly basis, and not only will you skinny out, but you'll add a decent amount of strength in the process. For chins - in the 15's and 10's if you can't do concurrent reps, cluster them - and in the 5's and 3's, add weight if possible using a dip belt or dumbbells held in your feet. You should be able to find all kinds of info on initial loading for the lifts and how to transition between rep ranges in the FAQ's if you need it.
Hope that helps.