A few comments....
adding timer code will be easy, maybe less than a dozen lines of code.
To keep it simple, wait 10th/sec with each pass of the loop, that way our push buttons still work fairly quickly (arduino will seem to sleep during the delays so keep them short).
example: delay(100); // delay 10th/sec 1000=1 second
Keep a counter and when it hits 1 minute, do your thing....
counter = counter + 1;
if (counter == 600) // 600 10ths = 60 seconds = 1 minute
{
digitalWrite(LED1, HIGH); // turn on LED
digitalWrite(RELAY1, HIGH); // click on relay
counter = 0; // restart our counter
}
maybe a we bit more detail to determine if we are at 1 min or 5 mins with this time through the loop.
I would say turn on at 1 min, off at 2 mins, on at 7 mins, off and reset counter at 12 mins. Does that sound right? (I recommend only waiting a few seconds until you get it counting properly and then bump it up to minutes - to keep you sane!)
Comment #2: Cut a power cord in half if you can not open the strip. The relay is controlling the power cord which is plugged into the strip. Make sure you have something solid to store this whole mess in.
Comment #3: Relays? Look around. They are in a lot of stuff. any old phone equipment lying around. I stole one out of some tossed PBX trash. It had roughly 32 of them inside and a paint-stripper/blow-dryer heated the back-side all of them fell out perfectly desoldered.
Comment#4: You could use a 12 volt relay. The transistor can be powered by the same 12volts that powers the arduino. The control pin of the transistor is 5 volts from the arduino but it can switch 12v (exactly like those 2 web links suggest).
Comment#5: A 24vac relay will probably pull in at 12vdc.
The transistor+resistor+diode will fit on a circuit board the size of a dime (even using full sized parts). The relay is the only large part.
Any cheap 50-cent transistor will work. Steal one off the LED speed indicator from an old PC case. The resistor can be anything from 5k to 15k, exact values not required. You can test this stuff without the arduino. Wire up the relay electronics and hit the input with a 3volt battery from a PC motherboard. If it goes click, the 5v from an arduino will also work.
Once you have a controllable relay circuit, the arduino is simply the timed 5volt control signal.
One last comment... most arduino boards have an LED already connected to pin13. If you change the code to #define LED 13, you do not need to add an LED.