Severance and unemployment, do they overlap? after 5 years as a welding apprentice

I was offered severance of 5 weeks after being let go as a welding apprentice and I am unsure how it affects benefits. There are 5 people counting on me, so I am trying to be careful. 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.