Hi A.,
I feel for you in regard to the sleep deprivation, especially with being a single mom. Unfortunately your pediatrician gave you bad advice to let your baby cry it out. At 5 months, and even up to 2 years old, babies are often not developmentally capable of sleeping through the night. Forcing that on a baby by the cry it out method is neglecting the baby's most basic needs, such as hunger, comfort, and a secure attachment to you. When you respond to her cries you are teaching her that she can count on you to be there when she needs you. Not doing so risks her withdrawing and giving up. You risk her not being securely attached to you. I recommend reading Dr. William Sears' books, such as The Baby Book and Attachment Parenting. Another book called The No-Cry Sleep Solution may also help. Keep in mind that growth spurts, teething, developmental milestones, gas pain, illness, separation anxiety, and any number of things can effect a baby's sleep patterns. Go to her every time she cries, hold her, keep the lights low and be quiet, feed her and change her if she is wet, and rock her back to sleep or whatever works to get her asleep again. You might also want to try co-sleeping or bed sharing. You can bring her crib in your room or have her sleep right next to you with a safety rail on your bed. This is the norm in most countries in the world, and Dr. Sears' books will help you understand the benefits to both your baby and yourself. If she is teething, put a couple of Hyland's Teething Tablets in her mouth when she wakes up. Good luck, and blessings to you!