
Unless it rises to a deportable offense, if the probation and conviction has been completed more than 5 years ago, it should not prevent naturalization.
See our articles below on naturalization and the connection between criminal and immigration law. I would advise the use of an attorney to ensure the crime does not arise to a deportable offense prior to filing.
http://immigration.lawyers.com/blogs/archives/10959-Requirements-for-Naturalization.html
http://www.avvo.com/legal-guides/ugc/connection-between-immigration-and-criminal-law