Got severance, how does it affect benefits?

I was offered severance of 5 weeks after being let go as a nurse's aide and I am unsure how it affects benefits. I am in Buffalo, in case local advice matters. The agreement mentions a release and a payment schedule. Who should I ask before signing?

Thanks for writing this out. I went through something close to it last year, and it got easier once I kept a simple log of every call and form.