This sounds like it could either be a short in the solenoid itself or a short in the ignition switch or left control switch. I'd check the wiring under the front panel first for any obvious shorts that might be causing the solenoid to trigger,plus the solenoid itself can short out internally and cause direct power from the battery side of the solenoid to power the starter wire.Plus the solenoid on the 2005 700 efi has an updated part number.They usually do this for a reason. Should be the same as yours. Item #13.Dirt Cheap Yamaha, Honda & Polaris OEM Parts & Accessories – Cycle Parts Warehouse

 

Hey MYWAYOUT, Thanks for the post. Looking like this might be my issue as well.

How much of a job is the replacement process?