The tachometers are accurate even after all these years. Check your's in the morning when you first start the car and stay in park, it will idle about 1300 RPM and then after 15 ~ 20 seconds or so (depends on ambient temperature) the RPM will drop to about 800.
I do not know what the original rev limiter is set at, but 5,000 RPM is certainly not right, so the car my be cutting your RPM because of the faulty codes. Go to an auto parts store and scan the car. Get the exact DTC numbers and correct those faults before trying to mess with the tach.