Intel T5450 Processor 1.66GHZ

The processor itself is 64-bit capable, but it's impossible to answer the rest without knowing what system you have.  It's a bit like telling someone you have a 4.5L engine and asking if you can tow a trailer with it - it depends on whether the engine is in a Jaguar or a Ford truck.

The processor itself is 64-bit capable, but it's impossible to answer the rest without knowing what system you have.  It's a bit like telling someone you have a 4.5L engine and asking if you can tow a trailer with it - it depends on whether the engine is in a Jaguar or a Ford truck.

I have a Pink color Dell Inspiron 1525, 2GB Ram, 1.66 Core2Duo processor. Is that enough description for you to determine whether its a Jaguar or a for truck?

Can it run 64-bit Windows?  Yes it can.

Is it worth running 64-bit Windows as is? Not at all - with 2G of RAM it'll actually be slower than 32-bit Windows, and you'll see less free memory.

Is it worth running 64-bit Windows were you to upgrade to the maximum 4G of RAM?  Probably not - though you'd see all 4G, the larger kernel size means you'd likely see less free RAM than you had under 32-bit Windows.

When you have a system capable of going to 6, 8 or more Gb of RAM, 64-bit Windows makes sense.  For a system limited to 4G, it doesn't - at best the added RAM use will be offset by the larger footprint of the kernel and programs - so you won't see any net benefit.