My recommendation is for you to try it first on a variable gain amplifier. It seems to me that you are using a fixed gain amplifier, whose gain is derived from calculations. However, in practice, the ideal gain is not exactly achieved, because of the imperfections in the circuit that are usually neglected. Like for these case, I think the imperfections here are those in the op-amps and the unexactness of the resistor values (it has tolerance around a nominal value). If you use a variable gain amplifier, you can practically tune it in the actual circuit and, by trial and error, find the appropriate component values to meet your required gain to amplify 0-50mV to 0-5V. I suggest using an instrumentation amplifier, whose gain can be tuned by a variable resistor. BTW, in-amps are also good for purposes of isolation.