Hi,
Yes i've seen a problem very similar to this yesterday too
Anyway, here is a minimum parts count design just to show how a circuit like this might be made. Since there are available plus and minus 15v supplies this is quite simple, however in the real world you dont get that anymore (maybe in the 1970's or 1980's you got +/- 15v supplies but these days you're very lucky if you have that kind of power supply available).
The approx 54.9k resistor comes from knowing that 273ua will be flowing and we have a minus 15v supply to bias with to create zero volts at the non inverting terminal of the buffer op amp. That solves the zero point problem, but unfortunately that unusual value does not happen to also give us exactly 5v for 373ua input, but instead gives us almost 0.5v higher (5.5v almost). Wouldnt it be nice to have a 50k resistor there instead, so that the extra 100ua means we get exactly 5v at 373ua input? To make up for that we simply calculate a resistor value that, in parallel with the 54.9k resistor, comes out to exactly 50k, and run the other end to ground instead of -15v. This way we get our zero voltage point satisfied and we get our 5v point satisfied too. The approx value is shown on the schematic attached (approx 555.56k). You can note that this extra resistor works only at currents above 273ua because right at 273ua that node has zero volts to ground (by design of the 54.9k resistor) so there is no current flowing though it until the current goes above 273ua.
Note that the circuit without the op amp produces the correct voltages all by itself, the op amp is simply a buffer.
This is just one way to do it. You'll also have to figure out the input bias compensation if needed.
Also in the real world we cant count on the power supply voltage being regulated well enough to use as a reference for making accurate measurements as the temperature drift is usually too much for that kind of application. That means most measuring circuits usually call for a reference diode somewhere instead of using the power supply directly.