Generally, when FXST--- models develop fuel leaks, the obvious divebombs are:

1. Vacuum fuel cutoff valve is stuck open or has a weak spring. Carburettor manifold vacuum pulls the cutoff valve open once it develops a vacuum. There is enough fuel in the carb for startup and initiation of manifold vacuum. Solution: replace the whole valve: once the vacuum spring gets weak, the diaphragm is next to go.

2. Leaky carburettor seals. Usually caused by the application of gasket sealant on the gasket, the sealant can dissolve and eventually leak. Solution: rebuild the carb but this time, do as the factory manual said and DO NOT apply sealant!

3. Kehin carburettor. As odd as it may sound, some '05's had Kehin carbs installed aftermarket in the hope of better starting and stronger top end torque. Not going to happen. Solution: Replace the carb with HD.