I've got a database with zipcodes. I must make use of the Google Maps API to look zipcodes during my database which are inside a 5 mile radius of the local zip code I enter.

For instance, I place in 33180. I wish to retrieve from the database all of the zipcodes/areas near to 33180, using Google Maps API.

QUERY * FROM zipcodes WHERE zipcode=zipcodes within 5 miles of 33180 (produced by Google Maps API)

Is possible with Google Maps API? How can i start if that's the case?

You cannot do that using the google maps api alone, you'll need some server side language to question your database.

Tutorial compiled by google:

http://code.google.com/apis/maps/articles/phpsqlsearch.html

Only use a local zip code database (like this free zipcode database) that has geocoded all zip fasteners in america. Then, just write a question that does the easy lat/lng distance calculation and returns the very best N results. This can run so much faster than using Google's API, and also you will not need to bother about daily API limits.