I'll assume your backups are dump files. In which case, create a new repository using
svnadmin create /path/to/newrepo
Load your freshest backup into it using
svnadmin load /path/to/newrepo < backup.dump
This will fill the new repository with all the revisions included in the backup.
Now you need to transfer over the newer revisions from your current repository to the new repository. To do this you need to dump out the newer revisions from your current repository and load them into your new repository.
To make the example a bit easier to understand let's assume that your current repository is at revision 1500 and your backup only contained 1250 revisions. So you need to dump revision 1251 to 1500 from your current repository and load it into the new repository. To do this you need to run
svnadmin dump /path/to/currentrepo -r 1251:1500 --incremental > additionalrevs.dump
svnadmin load /path/to/newrepo < additionalrevs.dump
The --incremental flag is essential
Now in case your backups are file based backups containing the repository files on the server side, you may be able to get away with another trick. Make a copy of your current repository because we will be changing files in there and things can go wrong. Find file /path/to/repo/maindir/db/revs/0/42
in your backup and copy and replace it over the same file in your copy repository. Do the same replace using file /path/to/repo/maindir/db/revprops/0/42
. Once you do this verify the new copy of the repository and there's a chance that the problem could be fixed.