Scaling signal voltage from 0 to 5 V
I have a very good 5 V input


If your "very good 5V input" is an ADC input with sufficient resolution AND accuracy I wouldn't bother rescaling. Converting a span-range of 2.6 volts to a range of 4 volts is like adding ADC resolution of less than 1 bit whereas, if you you sampled the signal 4 times and averaged, you will likely obtain 1 bit increase due to what is known as ADC process gain. 

This works if you can oversample the signal by 4 times.