If the plea deal ended in July of 2009, you must wait 5 years to be safe before you apply for naturalization and also if I were you I would not travel outside the US. Theft is a CIMT-Crime Involving Moral Turpitude and it can make you inadmissible, i.e. not eligible to enter the US if you depart and upon return to the US, at the port of entry, you may be placed into Secondary Inspection and unpleasant things may occur such as the officer confiscating your green card and issuing you an I-94 parole document valid for 30 days with an appointment to the Deferred Inspection office where they may issue you a Notice to Appear (place you into immigration court charging document). Even though you pled and got probation and its a misdemeanor if you pled guilty to get this probation from the prosecutor you are still viewed as having a 'conviction' for immigration purposes. Whether this qualifies for a petty offense exception, please call us or other colleagues to arrange for a consultation.
You're better served starting your time calculation from the date the case concluded (July 2009). And then add your five years but only if you didn't have any probation violations and your probation was terminated successfully. Or you can try to vacate the plea of the petty theft case, get the case dismissed and then apply.
The case did NOT "ended on July 2009" if "there was 1 year of probation". The case ended whenever the court said the case ended which is likely when you completed all the conditions set by the court, including the one year probation.
USCIS has a rule that states that an applicant for naturalization generally cannot prove good moral character while on probation for a criminal law conviction.
You should collect all the court documents you can and review the documents and your specific facts with your attorney to see what legal options you have.