To display a clock on 5 x 1m strips of addressable LEDs using an arduino:

• Take a 5m length of addressable LEDs (WS2812B type) cut it into 5 lengths, stick them onto a plank of wood and solder the right hand side of the top one to the left of the next one down, the right hand side of that one to the left of the next one and so on.
• Take an Arduino Uno with ethernet shield (or an Arduino Ethernet )
• Download and install the FastLED library and the Time library.
• Put this sketch onto the Arduino.
• Connect the LED strip to 0V, 5V and pin 7 on the Arduino, connect the ethernet to the internet, plug in the USB and that's it.

Updated (December 2018) It now accounts for daylight saving time, changes colour every hour and shorting pin 12 to ground will turn the LEDs off - intended for use with a door switch or movement sensor.
Changing the colour scheme is very easy and it would be simple to use more LEDs for larger and clearer numbers.
Be sure to use a power supply with sufficient amps and connect it to the led strip, not through the Arduino's power socket. Flickering LEDs are a sign of low voltage.