Five month old terrible sleep

Alison, 🌈 👶🏻 born 7/26/19

My baby girl has never been a great sleeper. Meaning she’s never slept through the night ... well actually I take that back- twice in a row she slept once 9 hours a few weeks ago. But before that we’d put her to bed at 6:30 she’d wake at midnight and then every few hours after that. Then she hit the four month regression and was waking every hour. It was brutal. Here we are five months and we are back to that again. I guess I blame myself partly. I’ve never done cry it out as I don’t believe in it. So when she wakes I pick her up hold her rock her til she’s back asleep. Well I guess I’m paying the price now. She can’t fall asleep on her own. For a while I felt she was doing well with self soothing sucking herself thumb etc. now for the past week I put her down at 6:30 she’s up again around 9 something then again around midnight and after that every 1-2 hours. She’s formula fed and I’ve tried not feeding her bc I know at her age she doesn’t need to eat in the middle of the night. She’s a good weight and I feel like she’s doing this out of pure attention wanting to be rocked etc. at this point. I basically just rock her at this point and feed her bc it’s the only way she’ll go back to sleep. If I don’t and put her down drowsy she’s up again two minutes later and the cycle starts all over again. Our pediatrician said to do the cry it out / Ferber method. Start small and continue to let her cry for longer intervals. I’m at a loss on what to do. I could do it but I don’t love the idea but at the same time I can’t continue to live like this either getting one hour increment sleep. And my husband does help but this is hard on him too. We both have to work and it’s really been difficult to keep this up. Another thing is she is already trying to crawl so when she wakes up screaming the new thing is she’s on her belly , and can’t or doesn’t seem to want to go back to her back and acts like she’s stuck. But the weird thing is she’s going from belly to back many times. I think she really wants to crawl and is upset she can’t yet. She’s also cutting a tooth already so it could be pain from that. I tried Tylenol that didn’t help . We do a bedtime routine she has a sound machine I give her plenty of tummy time during the day I’m just at a loss. So many babies seem to sleep well already at this point. I just wonder if I am doing something wrong. Last night she slept from 7:30-10:20, 11-1:50, 2:25-3:30, 3:40-4:40, 5-6. Has anyone had similar experience?? How did you break this habit ?? Is it too late to sleep train at her age?