Yes, there could be. When you apply for naturalization, USCIS will look very hard at past criminal convictions. If they decide that your criminal record makes you deportable, they could issue a Notice to Appear and put your in removal proceedings. This can take place even though the conviction occurred outside the statutory 5 year period. You should have a local attorney assess the immigration consequences of your criminal history before you apply for naturalization. If you apply without be fully informed, you could end up in immigration court and attorney fees will be $5000 or higher (most likely).
An important factor is whether the crime is an aggravated felony. An immigration attorney would need to look at your certified court disposition in order to determine this.
Kindly note that this posting is offered for informational purposes only. It does not constitute an attorney-client relationship. Remember, this site is akin to an internet blog. Do not rely on information here to make important decisions in your life. Make an appointment to meet with a licensed attorney in his or her office (or via Skype or phone) to obtain competent personal and professional guidance.
Immigration consequences of criminal conviction depend on the specific language of the statute of conviction.
The information contained in this answer is provided for informational purposes only, and should not be construed as legal advice on any subject matter,not should it be viewed as establishing an attorney client relationship of any kind.