Hello AudioTrack,
Sorry for the late reply: my schedule didn't allow me to get back to Band-in-a-Box as quickly as I wanted 😊 !
Thanks for the screenshots of "Gimmie Five", the 5/4 demo track ... which is also a great example of polyrhythmic composition since if the rhythm expressed in particular by the drums is in 5 beats, the melody remains in 4 beats !
Clearly, the solution adopted by Band-in-a-Box for the drums is to position a beat every 96 MIDI ticks:
- In the list of MIDI events, the lyrics that underline the drum beats (1, 2, 3, 1, 2) are always separated by 96 ticks, or one fifth of the 480 ticks that make up a 4-beat MIDI measure (note: they are positioned a little before the drum beat, probably for display reasons).
[Image jointe de i.ibb.co]

- When you play the song by opening the "Big Lyrics" window, you can clearly see by looking at the scrolling of the lyrics (1, 2, 3, 1, 2) that the main beats of the drums are positioned on these 5 beats
[Image jointe de i.ibb.co]

Obviously, this system is not at all suitable for manually entering a 5-beat melody: since a measure has 480 ticks, you would have to enter the sixteenth notes at positions that are multiples of 24 ticks (480 divided by 5 then divided by 4), the eighth notes at positions that are multiples of 48 ticks, the quarter notes at positions that are multiples of 96 ticks, etc. ... while there are no clear markers for 5 beats in the measure!

And even if we succeed, the display of the melody in the notation window or in the leadsheet is unreadable because Band in a Box does not correctly display notes separated by gaps that are not multiples of 30 (duration of the sixteenth note in a beat of 120 ticks).
[Image jointe de i.ibb.co]

Lazy Bird