Reduce voltage by a constant 100mV
Something like this should do you. The required gain is span out/span in  = 5/0.15 = 33.33, so R1/(R3||R2) = 32.33. If we pick R1 = 100K, then R3||R2 = 3.09K. Pick R3 so that the output voltage is zero with 100mV in (and 5V reference). If your reference is not 5V, then you can recalculate R3 and R2. 







simulate this circuit &ndash; Schematic created using CircuitLab