Fuse No 5 on the earlier VII should be a 20 Amp, not a 15. These earlier bikes are better wired in some ways, Fuse 5 is direct from the battery and feeds the Start relay, you should never have a problem with it failing to crank (provided it hasn't blown the fuse). The later bikes late 2003/2004 have the start relay fed from a switched fuse so they suffer from "Startus Interuptus" like many other models, how do I know this, because my 2001 was wired direct. I couldn't understand what SI was about until one day I discovered there are two coils in the solenoid, the solenoid has an inrush current around 40 Amps (too much for a 15 Amp fuse).
Trace the wiring to and from Fuse 5
It comes straight from the battery, goes to the Start relay through the normally closed contact to the headlight relay.
Compare it to a later model.
Here the start relay is fed from fuse 4 via the ignition switch, a 15 Amp fuse will probably never blow because it has half a mile of tiny wire to limit the current and the ability of the solenoid to engage the starter properly. You cannot simply feed the start relay direct or it will turn the headlight on, there's several ways around that.