Here's the correct legal answer: five years, then it has to be renewed.
Although DBA's do expire we never renew them. They are really only required once to setup your bank account. Once you get past that point there is little use in renewing a dba or a local business lic.
In California a DBA ('Doing Business As') is issued and recognized when a local city government issues a business license to conduct business in that city. The license is renewed each quarter with a fee (In my city the fee is based on prior quarter sales). If the business license is not renewed, the rights and privileges of the DBA cease to exist.