Probably not. The 5000s are newer than the 3000s. And if newer CPUs are supported, older ones should also run. The problem is usually the other way around. You can also consult the CPU list at Gigabyte and compare it with the installed BIOS version https://www.gigabyte.com/Motherboar...

Hello,
Don't forget to check that the revision of your motherboard is :
B550M DS3H AC (rev. 1.0/1.1/1.2/1.3)
or
B550M DS3H AC (rev. 1.4)
or
B550M DS3H AC (rev. 1.5/1.6)
or
B550M DS3H AC (rev. 1.7)
and look under "Support" + "CPU Support" which will indicate which BIOS version you need, depending on your processor.