You can use googleflights to create a 5 flight itinery, and then follow through to the AA booking page and book it.
If you decide once at AA to do something which worked perfectly before - change the date or airport of one of those flights, or even just to force it to search again, it reports the error

Anything more than 2 flights on a single day fails on the AA site, but works when a-n-other external system feeds past that checkpoint - so it's clearly a "bug", although whether they'll fix it ...

Trying to pull apart the parameters and see what contributes to URL gives
&c=
MSE {main search engine}
&GFS {google flight search}
&20180601 {yyyymmdd}
&DST {timezone}
&DST {timezone again}
&WEB&
&IIIII {flight classes}
&IIIII {flight classes}

But this I cant get broken down
&bookingPathStateId=nnnnnnnnnnnnn-nnn
which seems to relate to the flight numbers somehow