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Hello, thank you for the question.
Three weeks is a low for 5 years of service. It could be more depending on your position, age, and the job market in your area for your skill set.
Of course, they give you a very short deadline to accept their offer. They don't want you to take the offer to a lawyer. I see it all the time. I recommend that you take it to a civil or employment lawyer near you to write them a letter demanding more notice of termination or pay in lieu of notice. A local lawyer with experience in this field will have first hand experience with how the courts in your area treat such matters.
The only caveat is that if the entire company's operations are shutting down, perhaps they are bankrupt, it may be difficult to sue them. So don't delay in getting to a lawyer. Finding one isn't hard, and a short consult and letter to your employer shouldn't cost you much. If you have any employee benefits, then check them closely to see if there are an legal service providers there. That's not uncommon.
Is that a good start? I'll await your question or comment. If I've helped you I'd appreciate a positive service rating please.
I think you've seen what I wrote to you, does that make sense?