I'm licensed in CA only, and you should always check with local counsel. Having said that, you should contact an attorney familiar with the jurisdiction where your conviction was entered. Typically, a request for a dismissal of the conviction can be filed with the court, once probation has been successfully completed. Try going onto the court's website and search the types of forms available; search the term "expungement". Good Luck & God Bless.
The answer provided by Judith Fouladi is incorrect. If you were convicted 5 years ago, you cannot now ask the court to dismiss the charge. A recent change in New Jersey's expungement statute has reduced the waiting period to make application for an expungement from 10 years to 5 years. The waiting period does not begin to run until you have successfully completed your entire sentence, including any period or incarceration and/or period of probation period. Please also bear in mind that certain charges (usually violent crimes) are prohibited from being expunged by law. You have not indicated what the charge was, so I cannot give you a specific answer. Assuming your charge was one that qualifies under the Statute, you will have to wait 5 years from the date you completed your probation. An expungement is a rather complicated procedure. I suggest that you contact an attorney licensed to practice in the State of New Jersey and provide him with more details so that a determination can be made as to whether you qualify for an expungement at this time.