Samo, she will lose body fat. It's not about weight, it's about body fat. But the real results won't show until after she has the baby.
MT, it's possible and safe, but ONLY with your doctor's approval. The main thing is to focus on eating healthy by changing your eating habits. It's possible to lose unhealthy body fat while gaining healthy body fat needed for the baby. Find a good exercise program that isn't strenuous on you and the baby. I was doing kickboxing before I found I was pregnant (also 5 weeks like you) and now I have toned it down to walking daily and doing a workout program by Gabrielle Reece's personal trainer. I'm not focused on losing weight though, I'm focused on being fit for the baby. Being overweight can really hurt the baby and I want to make sure #3 has a great start. Hope this helped
ETA: The best thing you can do is to focus on maintaining a healthy weight (talk to your doctor about how much weight you should gain) by eating what is right, after you have the baby, you will see that changing your eating habits and exercising was very beneficial. But please talk to your doctor. And remember, you're not trying to lose weight, you're trying to stay healthy. Don't get in the mindset of trying to lose weight because you can fall into the trap of dieting. Which is NOT good for the baby or you at all.