Severance and unemployment, do they overlap? - what worked for you?

I was offered severance of 5 weeks after being let go as a school bus driver and I am unsure how it affects benefits. I have read a lot of threads here and could not find my exact situation. The agreement mentions a release and a payment schedule. How did your state treat it?

Before signing, I asked a friend who is a lawyer to look at the agreement. It was a short conversation and worth it.