The official 10.5 installer should work, if it is not system specific. Look to make sure your official, is retail, as this tip explains. You have sufficient memory, you could install 10.6 from the currently sold 10.6 retail directly. So unless you are sure your applications are not 10.6 compatible, that might be the best option.
The disks shipped with a computer are typically specific to that computer and can't be used on another Mac. You have to buy a RETAIL version that can be used to install on any Mac. I'm locked in to OSX 10.4.11 Tiger because of 20 years of design work and records I didn't want to redo in different programs that worked on Intel Macs. The retail version of Tiger I had to purchase on Amazon was $225 but worth it as I've had to purchase several older refurbished Power PC Imacs.