Should You Apply For The Sapphire Reserve Or Ink Business Card First?

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Daniel B asked the following question in the Ask Lucky forum:

“For at least a month now I have been trying to figure out in what order to apply for some credit cards. I definitely want to get the Ink Business Preferred card with the 80k bonus. I understand that I can get it even if I am above the 5/24.
I am at 4/24 now. I was thinking of getting the Chase Sapphire Preferred (50k bonus) FIRST (which will put me to 5/24), then within a few days apply for the Ink Business, because that latter card I should be approved for even if I am at 5/24.
Please let me know whether I am correct with these assumptions?”

Since there’s a (mostly) right and wrong answer here, and since this is something that confuses many people, I think it’s worth addressing specifically. Most of the confusion here stems from the 5/24 rule: