YES, the ASUS M5A97 fully supports the FX-4350.
From your Motherboard Specification Page
Supported CPU's: AMD AM3+
FX™/Phenom™ II/Athlon™ II/Sempron™ 100 Series Processors
Specific CPU Support: https://www.asus.com/Motherboards/M5A97_R20/HelpDesk_CPU/
(The FX-4350 is supported since BIOS revision 1006)The board should ship with the correct BIOS
, but in case it doesn't you can download it to a USB drive, plug the USB drive in when you first start the computer, boot into your BIOS when the PC starts up for the first time, and then navigate to the BIOS update section. You'll be able to tell the BIOS to update from the USB you've plugged in.
The BIOS update (if needed) can be downloaded from here: https://www.asus.com/Motherboards/M5A97_R20/HelpDesk_Download/