The processor of course is. But the OS was not always full 64-bit, and yours will not enable 64-bit kernel but it can run 64-bit apps, lacking the memory benefit of the 64-bit kernel and lacking ability to install and use 10.8
The G5 was "'sort of 64-bit" but not fully, the registers were not 64-bit. The OS of course was not using 64-bit words and instructions.
A Mac OS X has been able to use up to 48GB RAM and with Snow Leopard and later that was increased to 96GB and 10.8 will allow up to 128GB RAM.
So unless you need the 15% booost in performance of 64-bit kernel, if you needed support for more than 32GB RAM which is the max you can physically use, you don't need 64-bit kernel. Whether you need Lion or later like Mountain Lion is up to you.
Snow Leopard was the first OS X that was a full 64-bit OS and you had 32-bit and 64-bit drivers, and issues. And the 2010 Mac Pro 5,1 was the first to default to boot 64-bit mode. 2009 with SL could be set to use the 64-bit kernel.
A little background
I'm sure you could find an article on www.wikipedia.com
you cannot change the EFI firmware. That controls whether it can use 64-bit kernel (it cannot, that code that ws in ML DP1 vanished).
You only needed Snow Leopard to have a 64-bit OS. ie, you can boot using a 32-bit kernel and still run 64-bit applications on top of it.
What you cannot do is assign more than 4GB to a process or thread or application which can help handle larger portions of memory on large data sets or files.
2008 and later modes has EFI64, an Apple derivative of UEFI specification. Those support 64-bit mode.
If you read the Apple articles on this subject, they assure you that you have a 64-bit processor. But that is not really the question most Users are really asking.
The real question is, "am I running the best and fastest and most memory and future-proof?"
The answer for Macs issued before 2008 is unfortunately, NO.
You cannot run 64-bit Kernel, which contains the 64-bit memory allocator, so you cannot address more than 4GB in any single Application.
Although it is not certain, many expect that 10.8 Mountain Lion will be inaccessible to Macs issued before 2008.
WOW Grant. The only reason I'm upgrading to Lion is for the ability to sync with my iPhone and iPad. And with this upgrade comes computer application compatibility issues and expenses upgrading apps like Adobe Create Suite, Filemaker, MS Office, etc. Other wise I was happy with Snow Leopard and MobileMe.
Now I have a new hurdle coming... Mt. Lion which if you are correct, my 2006 Mac Pro won't support it which means new computer time. ...
I wish I could give you and Hatter a "This Solved my Question" but Apple doesn't have that. Sorry... You both helped a great deal.
Dual boot. Keep Snow Leopard for when you work, and Lion for play.
iLion does not roar, it is a kitty with the iOS ification for devices come to desktop and most people like the iPhone or iPod and ease of feeling at home.
wait 6-12 months for ML to have legs. Wait for the 2013's if / when etc.
The only thing ML might have of real value to some is support for a GTX 680, nothing else.
This is what happens though when you tie the OS and hardware in a strangle hold. You can't use GTX 570 w/o 10.7.4 for one thing.
ps: I think Grant writes clear easy to read. I have that "b" and "d" use to look same or couldn't be sure syndrome when I was learning, and I still have to rewrite and rearrange when I try to write.
Thread Change (apologies):
Hatter, I read your replies with great respect and your reply above gives me pause. I was just about to update from SL to Lion (literally) ONLY because MobileMe is being terminated at the end of the month and I really need a way to easily sync my iPad, iPhone with my computer's iCal and Adress Book. If not for the demise of MM, I would not upgrade. I think the Apple OS has hit a peak and I'm any computing improvements are now a matter of the applications and not the OS, at least for me.
But when MM goes south, then what? So for the first time since starting with Apple in 1985, I'm having a dilemma of upgrading to the next OS. I always wait to see if there are any bugs, but always update gladly. But the cost of Adobe CS6, Filemaker12, Toast 11, MS Office 2012 is huge but are needed to be compatible with Lion yet the versions I have now do everything I need in SL.
I've considered syncing using Google but I'd rather have tech support that I can get at a Genius Bar or AppleCare especially in a totally new OS environment.
Because I have a Mac Pro, I have 4 bays each with a 1.5 TB drive so the plan is to mirror back up while in SL to bay 2 and 3 and and an external drive. Bay 4 is TimeMachine.
Then install Lion on drive 1 in bay 1. From reading RoaringApps, it seems some of my apps may work OK in Lion, like Photoshop CS3 is reported to work, but PS CS5 is iffy. We'll see.
Drive 2/Bay2 will be mirror backup for Drive1/Bay1. Drive3/Bay3 will be SL as I have right now to run legacy apps that don't play nice with Lion. I can mirror back this drive up to the external drive.
After much thought, that's the best plan I could come up with. But it boggles my mind that I am doing all this just to be compatible with a new OS I don't want, just to be able to sync using iCloud instead of MM.
Mountain Lion is a whole other animal that I haven't focused on at all until Grant's comments opened my eyes to what lies ahead.
I find it amazing that I'm so locked into syncing that I would go thru all this, but don't see any other way out as I need to sync my mobile devices.
I did not relish Google but after itunes 10.5 to get iOS 5 and the small screen iPod Touch I went to Android tablet. I prefer Google over iSync - even if there were not the issues with duplicates and issues with contacts and address books and Apple ID.
And I don't need to change OS though I will not install iTunes anymore on Windows except as a VM or something or that I only run (dual boot) IF I run into needing to (cannot imagine that happening).
3 could be split and clone partitions of each OS
4 for TimeM
2 for data
1 for both OS
lower optical drive bay SSD for your favorite OS
Thought CS5 works but CS3 is trouble??
Well.. re CS5 vs CS3, it seems to depend. I've been using RoaringApps.com as my source for what apps work or don't in Lion and re CS it's a bit all over the place:
Has Some Issues:
Dreamweaver CS3 and 5
Illustrator CS3 and 5
No Info either way:
InDesign CS3 and 5