I see that Zendesk only offer the customers with 2 options relating to CSAT, these are Satisfied and Not Satisfied.
As my company has its own developing code team, so I want to know that whether or not my company can create a CSAT function, which renders the customers be able to rate from 1 to 5 star, and then embed to Zendesk under Zendesk instructions?

You could build in your own link to an external rating system if you'd like. You could then provide this to users via a link in your business rules. You'll want to be capturing and reporting against that data separately as we wouldn't have a way of mapping your 5 star system to our CSATs in Zendesk natively.