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Checking the processor specifications, both the T5450 and T9500 seem similar but in fact are not. There are small differences that can cause instability in your system.
I recommend you checking with the laptop manufacture if the processor can be changed or if it is compatible with your system. We as Intel provide the hardware to Computer Manufacture but they design their own systems and set limitations.
As mentioned before, it seems similar but it may not be fully compatible with the system.