Is it possible to convert a file created in version 5.10 back to version 5.0? Can COADE do it if I e-mail it to you?

Afaik it is not possible. Maybe someone add coade has a way to do it?
btw: why would you?

In a perfect world it wouldn't be necessary. It's a long ugly story about a recalcitrant 5.10 and the vagaries of these machines on which so much now depends.

To a later version is no problem. To an earlier version is troublesome because the format for the input files changes over time due to new additions to the software. For example, in version 5.10 the format of the input file changed to add 9 new entries for hot modulus of elasticity. Also, a new #$Flanges section was added. If you delete these extra entries in the .cii file that you can create through Tools->External Interfaces->Caesar II Neutral File then you can reverse the process in an older version. Having said that, this isn't really something that we want to encourage or support. You can look up any of the old formats by looking in the External Interfaces section (Generic Neutral File) of the Technical Reference Manual for the versions involved.