So you were going 5 MPH over the speed limit and the cop stopped you for reckless driving? Why did he turn wide? If you are minding your own business going 5 MPH over the limit (which probably doesn't even register on a police radar) and you're well within your lane, who cares if he goes wide? And why would the cop make up a random speed (30+) when you were going identically 30? Story doesn't really add up. It sounds like an easy win in court because according to you the cop is just flat out lying about everything.
Don't cop cars have dashcam these days? I wonder if you could petition to obtain his dash cam video recording of you driving perfectly safely at 30 MPH.