You can say either "five-year experience" or "five years' experience" (see Raymond Murphy "English Grammar in Use" for intermediate students)

The technically correct answer is: 5 years' experience, because it's plural and possessive. Alternatively you would say 5 years of experience. If you worked for just one year, you would write: I have one year's experience. However, in the plural it's becoming more common to drop the apostrophe. If you look at job postings you'll see that many of them just write "5 years experience". To me this is perfectly acceptable.

I have 5 years' experience.