Hi,
When I turn it on, the voltage regulator outputs ~5v, but after some time (20-30 seconds) the colors in the LED's slowly changes for no reason and the voltage drops to ~3.2 volts.
What are your LEDs, it sounds like you are putting 5V across standard LEDs that drop 1.6V.
The colour change is due to them slowly burning out, the 3.2V is due to the increased current they draw as they die.
Can you please post a copy of your circuit, in CAD or a picture of a hand drawn circuit in jpg, png?
You description does not tell use the type of LED or if you are using current limiting resistor.
Have you put bypass capacitor around the 7805 as per the datasheet?
How is the Arduino Nano switching the "LEDs" ON/OFF?
Thanks.. Tom.. 