I'll join in with the dreaded phrase 'technical debt'; the longer you put this off, the greater the risk. One of the rules of business is that you prefer to minimize risk. So get a new production server, install the latest OS on it (which will include the new Perl), update everyting, and see how it behaves.

At some point, like tearing off a band-aid, you have to get started. You're already living on borrowed time with your existing server. There's a greater risk in doing nothing, rather than getting started.