5 week old won't sleep on back!!

After some suggestions. Thought my little girl didn't like the Moses basket so I've bought a sleepy head pillow and she still won't settle in that and as soon as I pick her up and lie her on me she falls straight to sleep. This is how she sleep most of the time through the night now.I think she likes sleeping on her tummy but I've read it's bad to put them to sleep like this. Don't know what to do!