At first glance it seems odd. Why wouldn't they just make the top horseshoe switch score 5000 without going through another switch? But I think it was designed that way to avoid that exact problem (missed scoring).

If the 5000 point switch fired the 5000 point relay directly, you would almost never get that other 1000 rollover. The 5000 would still be counting as it rolled over the 1000.

By tying it into the advance relay I think that hoped to eliminate this. The top horseshoe relay would close and then the advance relay would close, scoring 1000 and then your 5000 would score through your closed top horseshoe relay. The idea being, to get the 1000 to fire once and then 5 more times as opposed to the other way around.

The doesn't explain why yours keeps missing though. Maybe the timing is just too close and the 1000 is firing at the same time as the 5000. It would need to fire slightly before in order for it to work correctly. The 1000 should fire as soon as the advance relay closes. The 5000 relay closes at the same time but the 5000 doesn't start scoring until the motor starts moving and turns to the first cam. Is that enough time?

Or much simpler... maybe your 1000 point switch just isn't closing due to a dirty/open switch on the advance unit.