Correct! The Arduino I/O pins are 5v, and rated for 40mA (0.04 Amps) maximum. They are "signal" or "data" lines and they can't directly power anything other than one or two regular little LEDs. (With the right circuitry, they can control thousands of Watts, but they can't directly provide power.)
To power an LED strip you can use a [u]MOPSFET driver[/u]. The schematic shows a motor, but it will also work with an LED strip. Since LEDs are non-inductive, you can leave-out D1.
You'll need one driver for each separately-controlled segment. i.e. A single-digit 7-segment display needs 7 drivers and 7 I/O pins. You may be able to find a multi-port driver chip, but make sure it can handle the required current. (You notes say 5A 6A, but I assume that's for the full 5-Meters.)
And of course, your 12V power supply has to supply all of the required current.
...I recommend that you build one driver circuit and test one LED strip/segment (maybe with the Blink Example) before you build the whole thing.