Did some science at the factory:
The water takes approx 20 seconds from flow start to reach the end of the farm by the hoppers.
I have let mobs spawn in the farm four times, and then recorded the mobs fall and graphed the number of mobs fallen at intervals of 1 second, and summed them to get cumulative graphs.
I also summed the number of mobs fallen in all four cases to the bottom graph.
Based on this it should be possible to determine the ideal time that the flow should be running, if we know the mob spawn rate. Determining that would be tricky though, because you can't watch much of the spawning area at the same time, and it also depends on how many mobs there already are. But it appears that the water certainly shouldn't run for more than 80 seconds, and certainly not for less than 20 seconds, and that the proper amount of time would probably be between 40 and 70 seconds.
I guess setting the flush time to 50 seconds at 5 minute intervals should be a reasonable start. If the water takes 20s to reach the end, that should grab the mobs up to 70 seconds on the graphs.
As for how to set up a 5 minute hopper timer, Idk yet