Export Mail's Messages

On the blank POP accounts, yes they will be blank, ready for the OP to enter afresh her account details and therefore avoiding any corruption that might have been tolerated by the G5 but not by the later OS.

I forgot that about mailboxes. However, it is possible to export a mailbox (Mail > Mailbox > Export) after selecting each mailbox in turn in your G5 (Sent, Inbox etc.). Save them to somewhere you can get to from your new computer, eg., a CD or DVD. Then, in your new computer, launch Mail and choose File > Import Mailboxes.

That should work, making the reasonable assumption that the file format of Mail has not changed since your G5 days.