Hi,
to act as a "battery" 0.047 µF ( = 47 nF) are for sure way to low. The voltage rating of 5.5 V are indicating a super capacitor, but without a picture including the dimensions of the capacitor, which should be replaced, we can not give an adequate answer. So we can only guess, and according to the shown values you even migth use a MLCC in a 0201 package.
Is C305 the correct reference designator? I assume, as you have the BOM, you also have the schematic, which you might also share, at least a snipped including the capacitor in question.
BR