You obviously don't know what SOL is, that is the time from a crime happening, to when you can be charged. It has nothing to do with criminal records.
While most do not go past 7 years, and others 10, a criminal record report will go back forever, so your crime will always show up.
If it was truly done correctly, and you had a plea deal to drop the charges after then it should not show up. To be sure, go to the police station and pay for a report to be ran on yourself.
Remember you are suppose to answer honestly on questions on application