First, do the math. Find an equation which will take an input from 0 V to 5 V and produce an output from 1 V to 5 V. You probably want the equation of a straight line through two points.
The slope and intercept from that equation represent the gain and the offset for the circuit you want.
What other contraints do you have? How much current will the output need to produce? What kind of load impedance is acceptable for the input? What power supplies are available? How fast can the input change? What kind of protection is needed if the input goes outside the 0-5 V range?
Lynn
