DO NOT CRY IT OUT. read anything by the sears family to see why. www.askdrsears.com
however, your daughter is 5 months old, she could be teething. this will last until the teeth break through, and yes it is temporary, but it is HORRIBLE to have to deal with. it makes baby who is otherwise happy, a terror. i had one child in my day care who was completely unconsolable until his teeth finally broke through on the bottom, then mom tells me he did the same behavior through the top teeth breaking through. after those first ones, it is usually easier, although you will notice again some sleep troubles.
do your best to treat the pain with whatever your doctor recommends, i found that hyland products worked best for my son, and it is all natural. www.hylands.com
babies do not 'sleep through the night' like we expect them to, and the best thing is to not expect too much from them to avoid becoming dissappointed in what they are. sleeping through usually means 5 hours tops - remember they have tiny tummies! i wouldnt really expect a kid to actually sleep 8 hr stretches regularly until after a year, when teething and that rapid growth and learning slows down. they will also have sleep disruptions with teeth, crawling, walking, and any other developmental milestone.
is there a dad involved? grandma? recruit help if it is too much for you. even a friend maybe who has kids can help - maybe switch off when each of you need a break. being a mom is hard work, no one will tell you its easy, and as they grow, they have periods of independence, followed by a period of dependence, and that is healthy and needs to be tended to. the more we are reasponsive to our childrens needs from the beginning, the easier it is to read them and their needs, and the easier it is to develop a relationship of trust and love with them. when you ignore their needs as a baby, you start ignoring there needs in general, and it becomes harder and harder to read what their true needs are. remember that - however, if you come to your breaking point, and your temper is flaring, and you feel like you might hurt yourself, or your baby, DO NOT HESITATE to let your baby cry. i DO NOT believe in routinely letting your baby cry, after all, who gets sleep when baby is crying, but do not continue to torture yourself or your baby to the point where someone is going to get hurt. get help from anyone in your life who is willing to help you before it becomes dangerous.
a baby crying in moms arms is still better than crying alone, so dont give up on your natural instincts to respond to your baby. you are the only person in the world who is given the power to read your specific child, you know what she needs best. but dont overextend yourself to the point that someone could get hurt.
you are a great mom for asking for advice, be proud of yourself for that, lots of moms are afraid to ask! keep learning and growing with your baby girl... you wont regret it!