If I was convicted of reckless operation 5 years ago, can I already apply for my naturalization?

Generally, a single conviction for reckless operation of a motor vehicle five years ago will not interfere with eligibility to apply to become a naturalized U.S. citizen. A court-imposed order of probation from approximately 2012 - 2017 is quite unusual, however, and it would be wise for you to work with an immigration attorney who, after learning all of the details, could advise about eligibilities, options and strategies to attain your goals, and who then could offer legal representation in the often complex application process.