S.D.
If you're breastfeeding, which is best for the 1st year, then breast milk digests much faster than formula, so the baby gets hungry more often (every 1 1/2 to 2 hours.) Even if you're feeding formula, you baby is very young still (5 months,) so it is very normal for the baby not to be sleeping through the night. Every baby is different. She may start sleeping through the night, then start waking up again because she is teething. You can't spoil a baby that small. If she is hungry, feed her. Next month, you might start introducing solid foods (baby jars of baby food) and that might help keep her fuller longer. Don't put rice cereal in bottles. Only feed it with a spoon. Talk to your doctor before you start solid foods.
A really good book to buy is What To Expect The First Year. It has just about every question a parent could ask in it, and the answer. The questions are age appropriate for every month of the baby's 1st year.