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Is it too late (or even necessary) to try Public Accounting?

I've worked in private accounting since graduating from college a little less than 5 years ago, and have worked for three companies. I got my CPA in private industry 2 years ago. I started out as a staff accountant at a large public sporting goods retail company, moved to Senior Accountant to a large multi nat Aerospace co, and am currently a Senior Accountant at another Large publicly traded Aerospace manufacturer. The job pays 80, approx 50 hrs per week, sometimes weekends. 

I enjoy my job and I enjoy manufacturing analytics. Question is, at this point is it too late (or even necessary) to go to public accounting? I am concerned that not working in public will affect my prospects for management positions going forward. Someone give their two cents….