DUI Conviction VS Citizenship

One of the key requirements for Naturalization is "good moral character." You have to establish good moral character within the 5 years prior to filing the N-400 but USCIS may look to periods outside of 5 years as well if there are repeat and multiple violations. Also, generally speaking a simple DUI does not lead to a finding of a lack of good moral character and should not impact the naturalization process. These are state law questions that interplay with federal immigration laws and as such you would be wise to speak to an immigration attorney before filing your N-400. Not to scare you but there are situations wherein people with certain types of convictions depending on the timing of the same could not only be found ineligible for naturalization but the government may actually start removal proceedings.

I hope/expect that you disclosed your DUI to the USCIS when you applied for permanent residency since it looks like the DUI occurred prior to the grant of permanent residency in 2004. In any event, different USCIS jurisdictions view DUIs as lack of good moral character without further review or not a lack of good moral character so long as it is not reflective of other problems. If it has been 5 years from the date of conviction and if it was a single incident without injury to others, then you should be able to naturalize, if everything else is in order. You will need to provide a cretified copy of the court disposition.