Hi @hbmg as usual, if you have any important data, please backup first.
What I will suggest you to do is to try updating your laptop to the latest bios possible.
to really support, it really depends on the bios, what i do is normally i will compare the specs of what it can the laptop mainboard can support the processor, e.g.
listed on the website of the configuration,
https://www.cnet.com/products/sony-vaio-vgn-fe31b-15-4-core-2-duo-t5500-win-xp-mce-1-gb-ram-80-gb-hdd-series/
http://www.computer-specifications.com/specifications/Sony-VAIOVGNFE31B-Specs.html