I did a 32 to 64 bit conversion on Debian, which is the only distro I think you can actually hope to do that with (due to the very rigorous Debian apt packaging rules, and the exceedingly robust apt tools), and even there, even though it technically worked in that I did not reinstall the OS, it took so absurdly long to do, and required so many fixes, that my next 32 to 64 conversion I just copied over all the /etc files to backup and then created a filtered package list (filtered out lib files, which are generally dependencies of programs). Next I did a base install of a new 64 bit system, then I installed the package list. Then I used my backups where needed to update the configs and various other files, but note, you do NOT want to just blindly reuse your 32 bit configs, since you don't know what has changed or might be different in 64 bit. Both methods are tedious, but I would never do the 32 to 64 bit crossgrade again, although it was interesting as a test just to confirm it can be done. But even there, most of the configs ended up needing to get purged, so it really was not super different from just rebuilding a fresh install from a package list, which is how I did my second cross-grade.
With rpm/CentOS, I'd say your odds of hitting the best case scenario I cite above, where you do technically preserve the install while cross grading to 64 bit, are very close to zero, and you'd certainly regret it afterwards in terms of the time you spent.
I disagree with the person who says if 32 was what you started with, it's probably still ok, that was not my experience, PAE (> 4gB) ram support in the kernel was and is getting more buggy, so you were limited to 4gB stable ram, although I ran more using PAE, but it had increasingly bad stability issues because basically almost nobody uses that in the real world, so the bugs were getting worse and worse in the kernel support by the year. Also, certain applications were not getting supported in 32 bit any longer, and that was also getting worse by the year, which is why I finally dumped my main 32 bit systems.
As an aside, the reason you can't find anything on that conversion for CentOS is that there is no way rpm/CentOS can handle it, particularly not from that era. You can find several decent how-tos for Debian, but even those are quite optimistic, as I discovered, and very very picky and complicated, but theoretically possible because of how robust apt is.