Baby sleeping on stomach

Any moms have their baby sleep on their stomach? It makes me so paranoid but that is the only way my baby sleeps. I have a 5 wk old and have literally held her 24/7 because she would scream anytime being put down. She would wake up crying within 10 minutes of laying her down on her back. She hates wraps so it's not like I can wear her and get stuff down either. So I've discovered the only way she will nap is if I put her on her stomach. I watch her like a hawk every second on the monitor though. She still sleeps on me at night because I'm scared to have her at night on her stomach just yet when I'm not watching her constantly. She is strong enough to pick up her head and turn it side to side also. Any moms have experience with dealing with a baby like this? And what did you do about it?