I am looking for bluetooth headsets for a Nokia C5-05 phone. Will BH-108 and BH-112 headsets work well with it?
Yes,both the headsets are compatible with your phone.
Source :- As seen from online retailers and Bluetooth version of headset.
it should work with bluetooth enabled Nokia mobile. but there can be incompatibilities
Nokia Mono Bluetooth Headset BH-108 - How do I know that there is an active link between the Nokia Bluetooth Headset and my mobile device
Once the connection to your compatible mobile device has been established a green indicator light starts blinking slowly on the Nokia Bluetooth headset.
The headset is compliant with Bluetooth Specification 2.0 + EDR supporting the Headset Profile 1.1 and
Hands-Free Profile 1.5. Check with the manufacturers of other devices to determine their compatibility with
Bluetooth Yes, v2.1 with A2DP, EDR