If you are going to upgrade and the file opens fine on one of the two machines, why do you care since the file appears to be OK?
You might try running a recover of the file just to be sure.
You might also try trashing preferences on the machine that won't open the file.
What happens, when You try to open the files from another user of that machine? Did You do a vanilla install of the OS (clear the disk, then install from scratch)?
I'm doing some yearly work with FM6 on an older Mac, 10.6.8 - and this year, it did not start the fo5 files. All I had to to do was a restart of the machine (this Mac is running 7/24).
If the files open perfect on one machine and the files are identical, I would prefer to go for the current version (FM13). You could check the files one more time using windows. You can also do a test-run on FM11 (don't use anything older than FM11 for .fp7, IMHO).
When migrating from fp5, there will be some work to do... file references, commit in scripts, opener scripts and more - but the fm-solution should run fine after migration and finishing the 'to do's for migrating'. Take care about fonts - not all fonts are ok under current versions of FM..
Get the trial version of fmp11, migrate the files - and go straight forward to fm13 for doing the migration work. If You have access to MetaDataMagic, do the file-reference-fixer before migrating.
How many files does the solution have?