Severance and unemployment, do they overlap?

I was offered severance of 5 weeks after being let go as a sales associate 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. Who should I ask before signing?

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

Thanks for writing this out. I went through something close to it 9 months ago, and it settled down once I kept a simple log of every call and form.