Powering up LED strip - How many amps?
Usually strips have not individual LEDs, but are composed of a lot of "pieces" in parallel, and each piece is composed by three leds in series along with a resistor.

Usually the strips are composed by 60 leds/m (i.e. pieces of 5cm), but sometimes also 120 leds/m or 30 leds/m. Let's assume it is the 60 leds/m version (you can check the length of the piece you can cut - which should be 5 cm - and that it contains 3 leds).

This means that in 5m there are 100 pieces. Now, usually the 3528 leds absorb 20mA of current for each segment (the 5050 version should be rated at 60). This means that the whole led strip should absorb 2A @ 12V.

Now the power supply. 2A is the nominal current the whole strips should absorb. Add about 200mA for the nano, and increase a bit the current requirement not to stress the power supply: you get a 12V 3A power supply at least (note that, while 12V should remain the same, you can take any current greater than this value - if for instance you have a 12V 5A power supply it is perfectly fine).

Now, the nano. It surely can't handle the 2A current. This means that you can power the arduino nano from the 12V. BUT beware: you should connect the 12V power to the VIN input (so the onboard regulator lowers it to 5V). Then you can't power the LEDs directly from the nano, but you need a transistor to decouple them. You can take any nMOS with a drain current greater than 3A or an NPN with collector current >3A and build the appropriate curcuit to drive them, then connect the + terminal of the strip to the +12V wire, the transistor source (or emitter) to the ground wire and the gate (base) should be driven by the nano.