Will an iPhone 5 bought in USA work in Germany & the UK?

I'm presently working in Germany, and will be travelling to the US soon, and I need to know if an iPhone 5 (Unlocked) bought in the US will work in Germany and the UK. I currently have an iPhone 4, which works in Germany and the UK, perfectly. I understand an iPhone 5 is considerably cheaper in the US, but need to know 100 per cent, that it would work in Europe.

Yes it would but you might have to buy a different charger

Yes.

Well I know of a site that can remotely unlock your iPhone.
My friend and I got our iPhone 4 & iPhone 5 unlocked from that site.
It's called a factory unlocking process, and is easy. No jailbreak, no worries, unlock using iTunes

It's at http://www.officialphoneunlock.com
So after unlocking you can use with any GSM carrier, yeah and you can update your iOS anytime without fear of relocking it.