Can I sue starbucks for not letting me use the restroom 5 minutes after closing and I was inside starbucks for about 3 hours?

Sure, you can sue anyone for any thing.  However, you may be required to pay their attorney's fees under certain circumstances in addition to paying your own.  I suppose you will also have to prove damages and your question isn't clear about how you were injured or otherwise damaged in a way that warrants compensation.