"So, how do I tell the executable to look somewhere else?"
You set up symbolic links from where the program is looking to where the library routine is really located. For example:
ln -s /usr/lib/lib64/libstdc++.so.5 /usr/lib/libstdc++.so.5
At which point you may run into a problem with a program compiled to run on a 32 bit machine running library routines compiled to run on a 64 bit machine. Maybe not. You can try it and see if it works.
The ultimate solution is to compile the programs on the new machine.
Be prepared. Create a LifeBoat CD.