I'm not clear why you think you might have a claim on all 5000 shares. Can you be a little clearer about this? You didn't really share a timeline of your employment, so it's hard to reason this out from first principles.
Assume you get all 5000 shares. How much is that going to be worth? Low/mid/hi-how-many-figures?
(If you've got any kind of confidentiality agreement with your former employer, don't share details.)
If so, it sounds like you don't own the shares, but the company owes you the shares. The fact of whether or not you own the shares should be easy to determine. The part that's harder (and requires analysis of what you signed) is whether or not the company paid you what you were owed during the period of your employment (including, if applicable, shares).