Dell Vostro 1710 CPU Support

 Hello Dell Community,

I have an old Vostro 1710 currently running with an intel core 2 duo T5670, 4GB RAM and a 500GB 7200RPM HDD with Windows 10 on it. I use this PC for movies, school, and light gaming. I wanted to know if I could upgrade the CPU to an intel core 2 duo T9600, as the T5670 is quite slow and doesn't even support virtualization. I've tried searching the internet with no luck. Which brings me here. Any help would be helpful, thank you in advance!

P.S: Will I need a BIOS update as well? I am currently running BIOS version A10 but can't update it because of the dead battery in the system. So this info would also help me out.