What do you mean by saying that the bearings are sealed "inside a race"? I do not understand the sense of word "race" in this sense.
I think John is referring to the larger bronze coloured bearing that is press-fitted direct onto the axle & sits inside the black circular "cup" that also houses the rear brake shoes. Phew, does that make any sense ?
The bearings I think you are referring to are the two sets of bicycle type that sit either side of the wheel. The cages that hold the bearings are an odd size and have proven unobtainable - although I am still searching for replacements.
In the meantime, I would suggest using the good one from the "outside" set and using that for the "inside". Then turn the C5 on its side and fit loose bearings where the "outside" set would fit. This will require more bearings (which is a good thing) and packing with grease (also good). The bearing collar will keep the bearings in. The only drawback is loose bearings when you next remove the wheel.
If this makes no sense whatsoever, let me know and I'll take some piccies to better explain .
The process worked very well on Steves C5 when his bearing cage collapsed.