You could say "al quinto piano DEL vecchio palazzo" (5th floor of THAT building) only if that was the only building there, or a remarkably recognisable one, but in this case "di un vecchio palazzo" (5th floor of ONE OF THE buildings that are...) is way more general, and it widely means "di uno DEI palazzi che ci sono vicino a..." For "vicino a piazza" generally in Italian you don't use articles for personal nouns, like for people names: "devo dire qualcosa A Marta" and not "devo dire qualcosa ALLA Marta", and it works the same for the unanimated things, like for the square: if you specify the name of the square, then you can't use the article LA (alla= a+la). But "alla" would have been correct without the name specification: "del palazzo vicino ALLA piazza in centro" Hope I made it all clear and easy enough