You're falling for the "we've constructed this machine to tell you no so you can't argue with us" ploy

Nah, that's bogus. It's a private company, they can do what they want. They could have absolutely given OP the 5/5 rating, and just had them sign something saying that they were content with the bonus appropriate to a 4/5 rating. No one would have had to receive a penny less.

That fixed budget is what they always say. The budget for the company is their problem, not yours.

Yeah, no shit, thank you for repeating what I said. The point being I never cared about the money and didn't even understand it was only about the money. I only wanted recognition.