Q: iPhone 5 in Spain

Are you talking about your network that you are currently using?

BTW  put you're phone to Airplane mode:  http://support.apple.com/kb/HT1355 

You can use it without problem. On the European Union, the cellular networks are GSM, so buy a GSM iPhone, although I think that Apple only sells GSM iPhones as unlocked in the USA

Ya

Without any problem because you can use it with the carrier you want, on Spain and on every country with GSM networks

You can buy an iPhone SIM unlocked in the US, but ONLY from an Apple retail store. It will work on GSM networks in EU, BUT the LTE MIGHT NOT work as they are different in the EU and the US.

Futhermore, the US warranty is NOT valid in Spain/EU.

¿Preguntas algo en este último comentario?

Hasta Leugo es buen viaje!

Todavía no hay ninguna red LTE en España, pero el LTE de los Estados Unidos y el de Europa es distinto. De cualquier forma, no puedes usar LTE en España porque no existe hasta este momento

I'm only learning spanish

No podras usar LTE ya que el iPhone de US usa bandas diferentes a las que (hasta ahora) se usan en los paises europeos que usan LTE.