Thumb sucker!!

How do I get my baby (5 months on September 8) to stop sucking her thumb? It's getting raw and sore, but she just won't stop! My method so far has been replacing her thumb with a pacifier every time she is sucking or going to sick on her thumb. I feel like she's living her whole life with a pacifier in her mouth, she laughs and makes baby sounds with it in. She can take it out and put it in on her own now so she's been spitting it out and just sucking her thumb, and I can't make her stop. Children can't be taught 'no' until 6 months old, so it's not like I can't tell her no or reason with her. Someone please help!