Make a note of the manufacturer of the 60gig drive, then fit it as slave in the old pc. Visit the manufacturer's website where you should find downloadable software which will enable you to clone the 5gig drive to the 60gig one. Then take out the 5gig drive and fit the 60 this time as master.
I believe Acronis will also do the cloning.
Beat the 5 gig drive to death with a hammer if you value your data security.
Not sure about the Win 98SE / FAT32 / max drive size question; off to do some Googling for you.