can i use an iphone 5 bought in the us in the eu?

That depends upon the model of your iPhone, whether you're using it in a roaming mode, and the communications protocol of both the iPhone and the country in which you want to use it.

If you provided more information, my answer would be different. For example, if you posted "I have an unlocked iPhone 5 model A1428, would it work in the EU?" My answer would read, "Your iPhone would work in any country that usesGSM, and if you have the appropriate regional SIM card."