An erection is 50% physical and 50% mental. And this is what happens to a lot of guys: They're finally with someone they really care about and that messes with their mind just enough to where it affects that part about sustaining an erection. And once you fail, it causes a little doubt to creep into your mind. Which makes the likelihood of failing again that much higher...and it becomes a vicious, self-perpetuating problem.
It's also compounded by the girls your age who don't really know very much about sex, in spite of what they think they know. They think just seeing them naked should be the world's biggest turn-on for a guy, and if you're not then they'll assume something is wrong with you...or with them. But actually an erection is a very complicated emotional, mental and physiological reaction, and a lot of little things can go wrong, at any time.
I have four pieces of advice:
1) Go to a book store and browse the Human Sexuality section. Find some (non-religious) books to read on this topic, and also about how to have "good" sex. Read them. Part of your problem might be confidence, and knowledge is a good confidence booster. Plus you may learn some things to do that will make her crazy for your even without actual intercourse.
2) For a week to 10 days prior to your next expected encounter, do not watch porn or masturbate. At your age, by the time you get with her your body may be so primed that it may be able to physically overcome any mental issues you're having.
3) If you're physically close enough to someone to be getting naked with them 5 times, you should also be emotionally close enough to openly discuss this with them.
4) And you should also consider getting a physical. Lots of things can affect your ability to get an erection, from your diet to your blood pressure. Discuss with a doctor. If he or she doesn't seem to take your problem seriously, get another doctor.