Hello everyone,
I have lived in Spain for just over 3 years now.
I have dual nationality, English and Italian, but moved to Spain as an Italian due to the issues with Brexit.
Am I correct in saying that after 5 years I can apply for a Spanish DNI and if so where?
Another question is, my residency card shows my previous address, where we were renting when we arrived, but we have since purchased a house. Do I have to get the address changed on the card and if so where/how please?
Many thanks in advance.

DNI- is for national identity which means Spanish citizen. You aren't Spanish. Like all nationals outside south America you cannot get nationality until 10 years ( unless married to Spanish) and you must pass language and cultural exam. You will have a green plastic card as EU member - you can change address if you want but it is not obligatory

You can apply for Spanish nationality after 10 years of residence (unless you're married to a Spaniard then it's 1 year) but you have to do a language and culture exam and in theory you must rescind all other nationalities you hold, although it appears to be enough to not use them for anything official within Spain or at the Spanish border. To be honest I'd say it's not worth the bother if you're an EU citizen, unless the country of your nationality is run by a party having a collective nervous breakdown blaming the EU for all its woes.

As for updating your details, you first update your address on your town hall's padrón then go to the police station with the updated padrón, form EX-18 filled in making sure you tick Modificación -> Por cambio de domicilio, and the tasa form stamped by a bank proving payment. You'll also need to reserve a date and time at the police station.