Well all of the sleep training books, including Ferber methods, are going to tell you to put the baby down groggy but awake.
All of the no-cry methods are going to tell you to put the baby down groggy but awake.
Also, after she stops vigorously nursing/suckling, you have to detach her mouth from your breast. Just slip your finger in the corner of her mouth so she releases, then gently put your finger under her chin to close her mouth. If she cries just let her attach again, then 30 seconds later remove it again. Continue until she doesn't cry anymore. (This is from Pantley's no-cry sleep solution).
Basically, she has to learn to soothe herself without you (the human pacifier). You can either try a different brand of pacifier that she might take (I like MAM brand). Or you can put her in her crib when she is tired but awake and let her cry until she learns to soothe herself (this is the ferber method).
Myself, I chose to take a middle of the line approach. You just need a plan in place since you can't bounce between crying and not crying.
While I think 5.5 months is old enough for sleep training...I do think that she is a little young to rule out night feedings all together. Usually around 8-9 months is when most will cut them out all-together.
If you are 100% convinced that she is not hungry, and doesn't actually nurse, just wants you, then I would go ahead with sleep training.
If she seems to get a little in her belly and goes right back to sleep and you are able to get her back in her crib. Then I might just play it out for a while yet until she no longer goes back to sleep.
I don't think the mobile will really help much...if anything, might just keep her awake.
When my youngest was sleep training at 8 months, we had the crib in our room so my older daughter didn't have to deal with it. Once he could sleep 11 hours by himself, we moved him in with my daughter. May not be a solution for you...but it worked pretty well for us.
Best of luck to you. Sleep exhaustion is the worst!