You would use FETs to switch the external 5V supply just as you would with a 12V supply.
You might get away with smaller lower power FETs than those normally used to drive 12V strips, which as often To-220 size. But I don't know any part numbers to recommend. All the small (TO-92 size) FETs I have seen that are available as thru-hole components would not have enough current capacity.
Series resistors will be required, and they will need to be high-wattage. It is always recommended to use series resistors for each led in parallel, but in this case you won't be able to do that. I guess the design of these strings relies on the leds being manufactured in the same batch from the same factory, so being as close to identical as is possible, and also they won't be designed to have a very long (many years) life.