Controlling a 5m LED strip with a Nano or Uno
You have a lot of LEDs that you need to power so lets run through the calculations. Assuming that they are RGB LED strips, ie 3 LEDs per physical LED:

5 x 60 x 3 = 900 LEDs


Assuming each has a current draw of 20mA, that is (900 x 20mA) 18A of total current if all are on at the same time at full brightness.

Since each colour will be controlled by its own FET, each FET will be required to drive 6A at full brightness.

The FET that you have is a Fairchild FQP30N06L 60V LOGIC N-Channel MOSFET that can drive up to 32A. Of course, that would need a large heatsink at that current.

If you plan to have any of the colours on at full brightness for extended periods I would recommend putting a heat sink on the tab to help dissipate the heat. 

The Arduino Uno/Nano uses a 328P microcontroller at 5V which, according to the datasheet, is suitable to drive the FET.

These FETs should do the job.