It is possible. You will need to seek a pardon. It is difficult to do but can be done. The nature of the crime is such that it is doable and the fact that time has passed if you have had no furtheer trouble with the law.
You will not have your right to own a gun restored with the felony prior.
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In Florida, getting your gun rights back is a long slow process, and there's no certainty that you'll succeed. You need to apply to the Office of Executive Clemency. The application can be found on their website. I highly recommend you contact a clemency attorney in Tallahassee. I filed one 4 years ago. When I checked on the status, which they don't appreciate, we were still way way back in the line. Good luck!