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Not sure what you mean by this but there is no such thing as a '5 years cooling off period'.Will this be refused due to 5 year cooling off period?
This is my history:
I had my first Tier 2 Visa from 1/11/14 to 01/12/14 then I switch Visa to another employer with new COS. I was granted tier 2 Visa from 04/01/17 to 22/01/20. In total, I have 5 years and 2 months.