Arduino Powering Multiple LEDs from External Power Source

Thanks for replying...if what I am saying is vague/not making much sense it is probably because I am pretty much a rookie at this so not actually sure how to successfully explain things...ill try and clarify.

So the beginning of the strip has two wires for power, two for ground and one for data - my initial set up had one power, one ground connected to the external 5v/10a power source (along with a capacitor in there) with the other ground, power and data wires going from the strip to the the arduino. Now, when I try this set up the LEDs and the Arduino do not seem to be receiving power.

When I remove the power source from the LEDs (where the capactior is in the picture) and plug it into my arduino they work but from what you have told me about regulator i do not think this would be a good idea when all the LEDs are wired up.

I have attached a couple photos too. Hope that helped.