How much should a five foot five inch woman weigh in pounds?

There isn't one ideal body mass for every height, simply because people have different muscle and bone structures. The desirable weight for an average woman who is 5'5", though, should be about 125 pounds. The formula for finding your desirable weight is by adding 100 pounds for the first 5 feet of height, plus 5 pounds for each additional inch. This means 100 + 5x5 = 125 pounds. Anything between the healthy BMI range of 19 to 25 (115-150 pounds) is considered healthy.

Sources:

http://health.nytimes.com/health/guides/specialtopic/weight-management/overview.html

http://www.nhlbisupport.com/bmi/