Will my iPhone 5 work in Europe?

Without more information it is hard to give an answer. Where are you from? You will want to talk to your carrier about an international roaming plan if you need to make phone calls. You can use wifi networks. Overall, yes your phone will work.

What model number does you iPhone have? Check Settings > General > About and look for model. If it says A1533 or A1457 or A1530 you iPhone is a GSM model which should work in Europe with european carriers but to be absolutley sure you should ask the carrier you want to use in Europe.

http://support.apple.com/kb/ht3939