5 gallons of 8.25% bleach in 13,000 gallons is 33 ppm FC so nearly 5 ppm FC per day which is quite high and unusual. You certainly wouldn't want to add that much at one time (unless you were doing a SLAM with high CYA).
As for FC/CYA experiments with algae, there weren't explicit experiments done with that. If that were to be done, one would need to use worst-case conditions with plenty of algae nutrients and optimum temperature and sunlight. What we have seen instead is numerous reports of failures and if you were to track those you see that the highest FC/CYA ratios for those failures line up just under the recommendations in the Chlorine/CYA Chart. This is why we lowered the FC/CYA level for SWCG pools because we consistently saw that those pools' failures were substantially lower than those in non-SWCG pools.
The original Best Guess chart was done by Ben Powell and it was mostly, but not exactly, correlating with the science though he used broad range categories so it could fit depending on what you chose within the range. I settled on starting with a midpoint fit and created a new chart consistent with the science that determines the active chlorine (hypochlorous acid) level.
As for scientific papers consistent with the FC/CYA ratio itself or more specifically where the active chlorine level is the relevant factor and not FC alone, these are listed in the "Chlorine/CYA Relationship" section of the thread
Certified Pool Operator (CPO) training -- What is not taught. All of the papers but one are consistent with chemical theory. The one that is not is the sole paper that looked at algae. It made no sense whatsover since the mechanisms for killing algae were no different than those killing bacteria, inactivating viruses and protozoan oocsysts, or oxidizing chemicals and is inconsistent with what we've seen from reports on this and other forums. Their paper shows green algae killed at 2 ppm FC at any CYA level up to the maximum 200 ppm CYA they used and that 1.5 ppm FC didn't kill the algae at any CYA level even 0 ppm and we know this isn't true in real pools. My best guess is that the growth media they used for the algae had ammonium compounds in them so that when they took the algae and added chlorine to it, they ended up with monochloramine which resulted in kill rates that were independent of CYA level (though the paper claims the growth medium was made to be chlorine demand-free). They also didn't measure kill rates, but mostly looked for binary complete kills with the way they did their tests. So maybe the algae itself had a chlorine demand of around 1.5 ppm so it would take at least that much for a complete kill. I tried to contact the authors of the paper, but never got a response.
The good news with the SWCG pools has been that their much more consistent and continuous dosing has shown that the 5% FC/CYA ratio is truly near the edge when algae nutrients are high. Between that control and use of accurate FAS-DPD tests, it's clear that the algae inhibition level is reasonably accurate. The non-SWCG pool 7.5% FC/CYA ratio probably has more fudge room in it but not a lot. Also, these algae inhibition minimum FC/CYA levels are only for green and black algae, not yellow/mustard algae. My best guess from the algae paper and pools with yellow/mustard algae is that it takes roughly twice as much chlorine to kill this algae so the minimum FC/CYA ratio would be closer to 15% to keep that algae from growing.
