As you can see the circuit is .....
This is way way more that an Arduino 5V line can supply.
Is there a solution to this problem?
I use the Arduino to toggle the LEDs off and on.
transistors, are they a possible solution as well?
That was not shown on the schematic you just had the LEDs going to a battery. Can you draw a schematic of what you actually have or want.
but do I need something like this: https://www.antratek.de/usb-adapter-5v-2a?gclid=COjfvKbIvcsCFQhuGwod7r0DLw
And if I need this one, how do I connect it to my circuit?
Connect the ground to the Arduino ground and the +5V to the +5V power supply of your port expanders.
1. If I do so, I don't need transistors, right?
2. What kind of port do I need for this power supply
3. Is it possible to supply my arduino with it as well?
Would the external supply deliver 2.5A to each expander
and would this circuit be parallel as well?