You need to state what processor (CPU) you have. That laptop model had several optional processors: some were 32-bit and some were 64-bit. Look in your system information or in Device Manager.

In addition to the (correct) answer from the first reply:

If you need a 64-bit OS, even if you have a Core 2 Duo CPU (with the EM64T extensions), the low RAM ceiling for this system (4G max) mean that it will be very slow going with a 64-bit OS, which has a much larger footprint than the 32 bit version.  

If your intent is to run a 64-bit OS, look for a newer system.  This one won't do, even if the CPU supports it.

I highly apologize for a very long response. I was busy with technology-related stuff, and it's best you don't ask why. Anyway, the CPU should be a Intel Centrino. Yes, you heard right Intel Centrino. The thing is 17 years old. Also, I found this at a resale store like 2 miles from where I live where I also got a functioning Dell Optiplex GX520 with Ubuntu.

Nothing in the BIOS menu.

I didn't say to go to BIOS. But, since you mentioned it, BIOS will show you the name/number of your processor, probably on the first tab beside a heading something like System Type.

You can also get the processor info. many other ways. Here are two:

Windows key > type PC or This PC > right-click the entry for PC or This PC > look beside System Type: it will tell you. For example, on my system it says "64-bit operating system, x64-based processor". If it says x86-based processor, that means it is 32-bit.

Or, Shift Ctrl Esc to open Task Manager > Performance tab > select CPU: that will tell you your processor.

Once you know your processor, Google it and open the link to Intel. Intel's specifications will list something like Intel® 64 or Instruction Set, and will say whether it is 64-bit or 32-bit.