fitting bearings to a shaft advice

[m_c]

Hi,
The difference as measured by a collegue (shouted across the room) is 5000th of an inch, or 0.0127mm in my world.

Are you sure he didn't mean 5 thousands? Aka 0.127mm.
In which case, it's going to be one very tight pressfit, which will most likely lock the bearing so it doesn't spin.