know these should have a current limiting resistor,
No you should not!
With high power LEDs like this you should be using a constant current supply, resistors just do not cut it.
The other thing is why you think this is a common cathode LED? There is no common connection at all. You could have done exactly the same as you are doing now with a NPN transistor or N channel FET.
Anyway that page says the device has a SMD 5252 Integrated Chip, not sure where but that is what it says. From bits of a data sheet I have managed to find for a QX5252 it looks like it is a switching regulator. However that does not square up with the 110 to 220V input.
What do you want to do with these LEDs? Are they for serious lighting? If so you are going to have to push a hell of a lot more current down them than 75mA.
This is my guess. The eBay seller hasn't got a clue what he has got, he probable just picked up a batch of random junk and this was in it. That specification looks to me like it was the specification of the whole finished lighting unit before it was pulled to bits. It looks like you just have five bare 1W LEDs. These normally take 350mA, so look for a constant current circuit that can provide that. Get two of them, one for each LED plate.