Should I negotiate my severance? - any advice?

I was offered 5 weeks of severance after 5 years as a logistics coordinator, and I have a few days to sign. I have been trying to stay organised about it. It includes health coverage for a couple of months. Did anyone negotiate and succeed?

Thanks for writing this out. I went through something close to it 3 months ago, and it settled down once I kept a simple log of every call and form.