There are so many threads in this forum regarding connectivity issues regarding Forerunners 305 (but many others as well) and Garmin Express. Just a small selection:
topic 1,topic 2,topic 3,topic 4
People follow all kinds of advice:
Resetting the watch, uninstalling Garmin Express, uninstalling USB-drivers, installing latest USB-drivers, removing watch from Garmin Express, using different usb-ports, using different usb-cables etc with no success and quite a lot of frustration.
I think there is a structural problem with several Forerunners (not only the 305) and the connectivity with Windows 10/Garmin Express. The solutions provided are cumbersome and not working. Please look into this.
Update: Recent problems seems to be related with Windows 10 systems.