FAA incidents only stay on your record for 5 years, then they disappear. I had a gear failure in 1987. It was classified as an incident. Ten years later I was sitting in an interview with United airlines. The question came up. I told my story, explained the incident, told the interviewer that the incident was no longer on my record but here is what happened. I gave them any and all "takeaways" I learned from it and that was that. I was sitting in a new hire indoc class two months later.
You can and must make these things into positives. I explained how we followed all of our emergency procedure, evacuated the aircraft, filed the required reports, worked with the FAA and CFR crews as needed ETC ETC.. just about every one has a bump in their past, either reported or not reported. It's okay as long as you're honest about it and turn it into a positive.