According to my source: http://ark.intel.com/Product.aspx?id=39311&code=t6500, the Intel® Core™2 Duo Processor T6500 (2M Cache, 2.10 GHz, 800 MHz FSB) features "Intel® 64." Intel® 64 is required for an Intel processor to support a 64-bit operating system.
Please note though, that if you are planning to use Windows* 7 when it comes out, the XP* compatibility mode is not supported by the T6500. If you are only interested in XP or Vista*, you should be fine.
I would double-check with Dell* as to which operating systems are supported on their Dell Inspiron* 15. They are going to have to supply you any 64-bit drivers you'll need if you choose to install a 64-bit OS.
Intel Customer Support
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