Why would you arm the approach that far off course? AIMEE is more than 16 miles from the loc antenna. The service volume is 35 degrees to 10 miles and 10 degrees to 18 miles. If you were 5 miles south of the loc you were outside the 10 degree service volume. My airline requires the localizer to be armed and captured before selecting the approach mode. I've seen the flight director do some weird things but arming an approach that far out is just asking for trouble.