Well, am a little surprised that your partition map is APM as all Intel machines shipped with a GUID partition scheme. According to my understanding GUID is required for an Intel machine to be able to boot from that disk. Don't remember back that far and it looks like 10.5 must have been able to boot from either.
With 10.6, you are not going to be able to install it unless the disk is using GUID. As you've seen it's just going to refuse. If you look at the bottom line in your shots of Disk Utility, you'll notice it has Apple Partition Map. That is going to have to be changed to GUID.
To do that, is going to require repartitioning the entire drive with GUID and consequently
"losing all the data on the drive". Creating a 2nd partition is not going to help you install 10.6 and is not going to "upgrade" your current installation of 10.5. Even if it would work, you would simply have 2 separate versions of OS X installed.
You will also not be able to do it while booted into 10.5.
This will need to be done from Disk Utility while booted from the 10.6 disk.
You have another (what I consider to be) really big issue to consider also, and that is the fact you are running your boot drive with <2% free space. That is dangerously low. I'd be totally surprised if you're not already seeing the spinning beach ball quite often, wondering why your machine is running so slow and possibly seeing it freeze on occasion.
looks like we were both typing away at the same time.
chas and I are at the opposite ends of the how much free space is enough debate - my recommendation to have a machine that is working as well as possible is a minimum 25% which would be 250GB free on your 1 TB drive. But his 50GB recommendation should keep you out of trouble and prevent freezing issues.