Honestly, I don't think trying to lose X amount of pounds in X amount of time is the best way to approach the fitness situation.
Is it possible? Yeah. Is it probable? Not really. Is it healthy? Not at all.
If you're looking to lose 20 pounds and truly stay at 160, I would advice for a more long-term, realistic(?) approach. I certainly don't want you to dissuade you from exercising; noble goal, and congrats. However, attempting such a feat in five weeks will likely result in overtraining, burn-out, and malnutrition (not really, but by my sketch estimates, you're taking in >1000 calories a day).
Eat when you're hungry, but eat healthy. Set up a nice, escalating training regimen and stick to it. This goes for both sides of the fence. Overtraining is just as bad as undertraining, IMHO. It definately leads to injuries (ask my hamstring).
Really though, I'm glad you're on the path. I'm also trying to drop 15 or so pounds, but I refuse to undereat, overtrain, step on a scale, or set a 'mission accomplished' date. When I'm happy with my body, I'll know what I need to maintain myself there.
Hopefully, someone who actually knows something can expand, or contradict my points. Best of luck, and remember to have fun. Bah, I thought I was done. You need to have FUN! It just doesn't go well without that element.
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