The factory ECU settings for a 2005 Ford Mustang's cooling fan trigger on the following coolant temperatures:
- Low Speed On: 216°F
- Low Speed Off: 208°F
- High Speed On: 228°F
- High Speed Off: 224°F
- Thermostat opening: 192°F
Therefore 208-216°F (98-102°C) is the desired engine operating range.
In extreme conditions up to 228°F (109°C) is acceptable for short periods.
Sounds like your fan is working as it should in low speed mode.
I suggest you merely drain the coolant, thoroughly flush the entire cooling system including the cooling passages in the engine itself, and replace with fresh coolant (Motorcraft Gold & deionized water). You could also add a "water wetter" agent that reduces the surface tension of the coolant and improves heat exchange.