Capital Gains on Home Sale

I bought a NYC coop 11 years ago as my primary residence, in Oct. 2020 I was laid off due to the pandemic, I then moved in Sept 2021 to upstate NY and moved in with family. I am now selling my coop and should close by Sept. 2025. May I take a $125K exemption based on living in the property for one year out of five since I was on unemployment and moved for a lower cost of living?  Do I need any proof beyond the unemployment records?