I live in Texas, but I work in PA for 5 months of the year and the office is located in NY. Which state out of PA and NY would I pay state tax to. What percentage will I pay and how much will be refunded since I'm a non resident. I'm only in the state for 2 weeks at a time.

You would pay PA income tax on income earned while you were physically present and working in PA. I'm not following what you mean by "I'm only in state for 2 weeks at a time" - what state are you referring to? NY has no claim on any income tax from you because it seems you neither lived nor worked in NY (the fact that the company is headquartered there is immaterial).

Income earned while present in PA should be reported to PA. You are part year resident.
You do not have any NY income. Your U.S. Tax Return: Working or Living in Two or More states