I went through this with my daughter--seems so long ago now. I read books by the Baby Whisperer which helped me. I too thought, "Oh my daughter just doesn't need that much sleep" but I was wrong. She sleeps more now at age two then she did at your daughter's age. It took awhile to get her back on track though. This method is not a leave the room CIO method. She will still cry but your there to help her by picking her up until she stops crying then placing her back in a sleeping position. Repeatedly---depending on the habits she has formed thus far you could do this many many times before she falls asleep.
First though, if she doesn't need to be rocked to sleep during the night, then she could probably fall asleep in the first place on her own at nap time too. Try using a simiilar routine during the day as at night but condensed. Maybe the room is too bright as well? I am a daycare provider and it seems like the children sleep sounder if I don't rock them completely asleep. It is almost like if you fell asleep in someone's arms when you come out of the first sleep cycle (approx. 45 min long) and you are not in arms anymore but in a strange bed you'd be disoriented too.
Also, if you are worried about daycare and her napping, she'll probably fall right in with whatever routine they do at naptime. That shouldn't be too much of a problem--I've had children start here that had one routine at home and a different one here. They know I'm not mommy and don't have the same expectations of me that they have of you. Your daughter, even at this young age, associates daytime sleep with being rocked by your completely to sleep and when she wakes and is not in your arms she is disoriented. It seems like you go in to her if she wakes up whether she is crying or just playing. If she is playing, let her go ahead, she'll probably fall back asleep. If she is crying try the "pick up put down" method from Baby Whisperer. Just be patient--it is hard--I nursed mine to sleep for naps and she used to literally suckle her way through nap time so by the time I got her in the crib she had already partially napped on my breast and was all full of milk whenever she didn't really need it in the first place ( I was mixing up her cues) My daughter fought me about changing this lovely routine because she had clear set of expectations about napping and sleep. I too was okay with this routine until I was about to start my daycare--I knew she and I needed a better one. Your daughter has a certain set of expectations too! Changing this will require Patience Patience Patience:) Hope this is somewhat helpful!
As for the cry it out method, at 5 months you might wind her up so much with crying it will have the opposite effect. Its much different to let a toddler whine for a few minutes than to let an infant scream for much longer periods--definitely recommend Baby Whisperer for a more gradual less traumatic method
