Got severance, how does it affect benefits? - any advice?

I was offered severance of 5 weeks after being let go as a customer-service rep and I am unsure how it affects benefits. It has been a long 23 weeks. I also wonder about the job-search requirement. Who should I ask before signing?

Thanks for writing this out. I went through something close to it 8 months ago, and it settled down once I kept a simple log of every call and form.