5/24 is referring to Chase only.

Every credit card issuing bank is got their own rules, 5/24 is Chase, meaning you can't get a Chase card if you applied for 5 cc (any) in the past 24 months, but this is based mainly on your credit pull, each time you apply for a Chase card or other cards, they will hard pull your credit one time, so if you got 5 hard inquiries in past 24 months you disqualify,  BUT, if you have good standing credit with AMEX, new Amex credit applications only soft pull, so this new application most likely not going to show up in your credit report, this is why I mainly focus on AMEX.

Citi cards, mostly allow you get multiple bonus on the same card, but they have either the 24 month or 48 month rule, meaning you can only get their signup bonus once every 24 or 48 months, also Citi doesn't like you have more than one of the same card, but sometimes there exceptions too, for example last year they introduced a new 5% card call customer cash, you get 5% bonus on any category up to first 500$ spending, during that promotion, you can change other Citi cc products into this card, so that sort of reset the counting clock, so you can apply a new card you previously got bonus for.

AMEX will not approve you if you applied and got approved 2 Amex cards in the past 60 days.

 If you read my post, this month I applied for 1 Chase, 1 Citi, 2 Amex.