Congratulations on your pregnancy! The fact that you already have kids it great--it helps to show that you can carry pregnancies to term.
Typically, after three miscarriages, the doctors will look into what may be causing them (it may be nothing but bad luck and/or genetic problems). In fact, many estimate the that miscarriage rate for the first 4 weeks is about 75% (however, most of these are never picked up, because the miscarriages typically happen around 4 weeks, when your period is coming anyway -- you'd never know you were pregnant if you didn't test early). So nothing may be wrong at all. Also, if you got pregnant back-to-back after your chemical pregnancies, you may be at increased risk for miscarriage. You're very fertile after a miscarriage, but you're also more likely to miscarry right after one. So that could have been a factor too.
It's great that you're now 5 weeks -- that means you're past the most risky first couple of weeks! Your doctor could test your progesterone (especially if you have other symptoms of it -- like bleeding before your period actually begins). But otherwise, I say hang tight and good luck!