Obviously, if it starts on five, then it should start on 6. Something happens out of control between one try and the next....
I would certainly test on contact C9 of the ECM
www.avigex.ca/xport/ignition31.jpg
www.avigex.ca/xport/chargingsystem.jpg
www.avigex.ca/xport/fusiblelinkh.jpg
or on the ECM side of fusible link B
(If necessary, I use a needle to connect to the wire through the insulation..then cover the tiny hole with silicon afterwards to prevent corrosion)
This contact comes from the starter solenoid. SHould read 12V when starting. That is not a big hint, but at least this is a thing that can be checked .